Ibn Ezra II
Moshe Ben-Chaim

The Ibn Ezra (Exod. 20.1)
"...The second category (of commandments) are commands which are hidden, and there is not explained why they were commanded. And God forbid, God forbid that there should be any one of these commands which goes against human intelligence. Rather, we are obligated to perform all that God commands, be it revealed to us the underlying "Sode" (principle), be it hidden from us. And if we find any of them which contradict human intelligence, it isn't proper that we should understand it as implied. But we should consult the books of the wise men of blessed memory, to determine if such a command is a metaphor. And if we find nothing written (by them) we (must) search out and seek with all our ability, perhaps we can fix it (determine the command). If we can't, then we abandon that mitzvah as it is, and admit we are ignorant of it".
In a previous article on the above commentary, "Ibn Ezra - Honest Inquiry", I quoted a Rabbi who explained this statement to mean that if we locate a command in our Torah which is incomprehensible, we cannot perform it. The following is a conversation which followed the posting of that article.

Reader: If we can't, then we abandon that mitzvah as it is, and admit we are ignorant of it". The Hebrew is "Nanichena kaasher hi, v'nodeh shelo yadanu ma haya..." I think a better translation would be "We leave that [mitzva] as it is, and admit..." "Abandon" leaves the impression that one would not have to perform or obey that mitzva which challenges our reason. We still have to obey it (cf. Shaul and Amalek). Of course, the example he uses is not a mitzva per se (U'maltem es orlas levachem), but a metaphor - which is clearly his understanding.  Otherwise, an opening is left for some to argue that any mitzva which does not accord with our reason can be abandoned.

Mesora: That is precisely what the Ibn Ezra means by his example of "Umaltem es orlas l'vavchem." That were it not for the understanding that it means to perfect the heart - not cut it out - we would in fact abandon such a vicious act as cutting out someone's heart, and not comply with even a Torah command, were it completely in coherent.

Reader: I would suggest that "leaving it (a command) as it is" does provide a new insight, to wit: We are obligated to fully explicate every mitzva - its particulars, structure and philosophical underpinnings. If we have exhausted our understanding of a mitzva and can no longer explain it rationally, then we revert to our position as avdei Hashem, humbly admit that our inferior intellects cannot fully understand this mitzva, and perform it - as servants - as our Creator intended.
"Nanichena kaasher hi' means we abandon (at least temporarily) further exploration of this mitzva, and perform it as is. (Perhaps years later another area of Torah will shed light on it, or perhaps a new idea will occur.)
On one level, this was Shaul's sin -  some of the particulars of the mitzva of destroying Amalek challenged his reason, so he did not do it (to his detriment). The navi's expectation was that he obey the command (by the way, the Torah says nothing about destroying the cattle of Amalek), and continue to probe the area if he did not understand. But his Kabbalas HaMitzva cannot be dependent on his understanding, otherwise Shmiras HaMitzvos becomes very subjective. I.e., people's intellectual capabilities differ and even the wisdom of their Rebbeim is not uniform. If the system allowed one to opt out when his reason dissented from a particular mitzva, then it is no longer binding. (Cf. Shlomo's sin, Sanhedrin 21b).
Thus, I would translate Ibn Ezra as saying:  "We leave the mitzva in its current state [of incomplete understanding] and admit... Descriptively - perhaps there is a p'tur of talmud Torah on this area - go study another area of Torah - until he can re-visit it. On the premise we agree - the Torah and mitzvos must be reasonable; the only issue is our understanding of the  Ibn Ezra on the response of the person to an area of Torah which, presently, is beyond his ken. I would say: Do the mitzva, move on to study another area, and keep plugging away at this one. That is Kabbalas Ol Malchus Shamayim. (Otherwise, there is no Kabbalas Ol - it is natural and proper for man to follow his reason.)
Mesora: Based on Ibn Ezra's words I cannot agree with your interpretation. He first writes, "And if we are not able, we leave it as it is," but he then continues, "and admit that we do not know what it was."
Regarding any of God's commands, if one does not know what action is required of us, it is impossible to perform - compliance with the unknown is impossible. This of course is so basic. But I believe Ibn Ezra's point goes one step further; obligation of the commands are based on some minimal level of comprehension. Torah is not a system of empty actions. Mitzvah - by definition - means that man acts with his body in accordance with ideas that appeal to his mind. He is not just a theoretician, but a philosopher and an activist. Following through in his daily activities is the only true barometer that displays mans' full agreement with God's ideals. But in a case where man cannot grasp what is asked of him, even by God, man is bereft of any method to observe such a command. The very performance is unknown, and impossible.
Your example of Saul and Agag is not an argument in my mind. Despite any emotional reluctance on Saul's part, it is clear what was meant by the command of "killing Agag". Saul did not say to Samuel, "I know not what the command meant." Conversely, Ibn Ezra's example is the Mosaic statement of "cutting one's heart", obligatory not on only a wicked Agag, but on the entire Jewish nation simply requiring rebuke. Taken literally, genocide is incomprehensible, certainly when the verse quoted ends with , "and your necks shall no longer be stiff." (Deut. 10:16) If one were to take the first part of the verse literally, to actually cut out everyone's heart, how can they be more submissive when dead? The latter part of the verse clarifies the former.
Moses, a just and fair leader sanctioned by God's inclusion of Moses words in the Torah, would never ask those not worthy of death to have their hearts mutilated. Ibn Ezra rightfully says in such a case where we cannot fathom the command's meaning, "we know not what the command is." This being the case, there cannot be performance, as you suggest.
I would agree that when we know an action required by Torah law, but we are ignorant of its reason, as was the case with Saul and Agag, we must nonetheless adhere to God's commands. This is only possible when we know the action required by the Torah. But when we are ignorant of even the very action asked of us, if we cannot even grasp the commands' structure, then there is no way we can perform it. This I believe to be Ibn Ezra's teaching.

Reader: Your point answers the question - The Ibn Ezra's examples are not mitzvos; they are comments in the Torah that, literally, do not make sense, and therefore require accessing our reason to understand and apply. They are not part of Taryag.

My only concern is that the impression not be left that Ibn Ezra was referring to some statement, concept, or entity which IS part of Taryag (the 613 comands). I would posit that there can be no part of Taryag that is beyond our comprehension, because, as you correctly state, if we don't know what to do, what kind of mitzva is it? It would not be commanding anything.

And you duly note that his examples are not mitzvos - as opposed to Shaul, who received an explicit command. (Not to belabor the point [Pesach is coming] - but Shaul argued that he intended to kill Agag in front of the whole nation, and that is why he brought him back to Gilgal - whereas the command was to eliminate Amalek entirely at once. He failed, and enabled Agag to procreate another child. He thought it would be a greater Kiddush Hashem to kill him publicly. Response: "Al tehi tzadik harbeh", "do not be overly righteous".