The Medrash states that Avraham asked Yitzchak what he saw and he answer that he saw the divine presence. However,when he asked Eliezer and Yishmael they both answered that they saw nothing. The passuk says that Avraham left them behind with the donkey. My question is, it is understandable that he left both Eliezer and Yishmael behind, but why leave the donkey which would be helpful carrying the wood for the altar?
Here's an old chidush of mine which addresses your question.
Many times, if not always, Neviim make a vague statement or perform an act which requires the person or people they are addressing to concentrate on the message. Leaving someone to figure it out themselves seems to be a practical way of having someone accept a message. So we find prophets placing their cloaks upon a new prophet, putting sticks together, telling stories about a poor man's sheep etc the list goes on.
Here, Avraham was hinting to Yitzchok what was going to be happening. He did this by separating the three items, the wood, the knife, and the fire between Yitzchok and himself. Yitzchok who stood to be consumed, received the wood, the item which also stood to be consumed. Avraham who was to act as the destructive force, took the knife and the fire. With this act he gave a type of hint to Yitzchok.
Rashi on this passuk points out that the words they walked on together mean Avraham was going just as happily as Yitzchok who didn't sense anything. By the next passuk, Yitzchok asks Avraham where is the sacrifice, to which Avraham responds ambiguously, Hashem will show his sacrifice. Rashi points out this was a way of telling Yitzchok if there will be no sheep, than you, Yitzchok will be the offering. Rashi again notes the second time the Torah mentions them walking together as meaning now they both went with the same degree of intent even though Yitzchok now knew he stood to be slaughtered.
So although the implications are that Yitzchok's curiosity was aroused simply by the missing sheep, I am adding that the first step to that awareness was the dispensing of the sacrificial items.
This symbolic act of Avraham was dependant on his placing the wood on Yitzchok, not upon the donkey.
Hope you like:)
There are meforshim who connect the חֲמוֹר with the word חֹמֶר (matter). This means that the entire location of the mizbeach was a holy place and only animals that were acceptable for korbanos could be brought there. This is similar to the halachos of the Bais hamikdash or the Mishkan.
I should note that Yishmael and Eliezer seem to have felt that there was no oddity in doing this so that it may have been the normal procedure. That is that non-sacrificial animals were never brought into the "sacred area".
Similarly, the mefarshim that speak of Eliezer and Yishmael being treated similarly to the donkey, place the emphasis on that. They do not explicitly say why the donkey was left behind. However, since the two were left behind with the donkey, it can be inferred that the donkey being left behind was the normal and expected behavior that did not need further explanaation.
As an example Aish.com discusses this concept (while explaining another matter) and brings the medrash
We recall the discussion between Abraham and Isaac as they headed toward Mount Moriah for the impending sacrifice of Isaac. Abraham looked up and saw a mountain with a peculiar cloud tied to the mountain. Isaac shared this vision, but the others who accompanied them saw only the mountain.
The Midrash explains:
[Abraham] saw a cloud tied to the mountain, and said: "It appears that that is the place where the Holy One, blessed be He, told me to sacrifice my son." ... He then said to him: "Isaac, my son, seest thou what I see?" "Yes," he replied. Said he to his two servants: "See ye what I see? " No," they answered. [Midrash Rabbah , Genesis 56:1-2)
Since the servants saw only the mountain, the physical reality, and not the cloud which represents the metaphysical, Abraham tells them to stay behind with the donkey. (Interestingly, the Hebrew world for "donkey," chamor, is related to the word for "physical," chomer.) Only Abraham and Isaac see the cloud tied to the mountain, and only they will continue the spiritual journey.