Your title would be better phrased "...why the mind perceives with more certainty than the body"
Yes, you are certainly in the ballpark. In order to perceive the "essence" of the wax, Descartes posits that the mind's understanding of the abstract properties such as "extension" "changeability" "moveability" and such are on a firmer footing for certainty than what is directly experienced through the senses. Descartes uses the wax example to demonstrate that what the senses directly experience are susceptible to deception because these perceptions are impermanent, e.g. a wax figurine or an ice sculpture may feel solid when it is cold, but will melt when warm. Hence we can ask - what was the essence of that thing which changed? It is still extended, it can change, when it melted it moved... but these are more abstract descriptions than say descriptions of the precise weight, color, smell or dimensions of the wax ball (or the melted wax blob).
Let us begin by considering the commonest matters, those which we believe to be the most distinctly comprehended, to wit, the bodies which we touch and see; not indeed bodies in general, for these general ideas are usually a little more confused, but let us consider one body in particular. Let us take, for example, this piece of wax: it has been taken quite freshly from the hive, and it has not yet lost the sweetness of the honey which it contains; it still retains somewhat of the odour of the flowers from which it has been culled; its colour, its figure, its size are apparent; it is hard, cold, easily handled, and if you strike it with the finger, it will emit a sound. Finally all the things which are requisite to cause us distinctly to recognise a body, are met with in it. But notice that while I speak and approach the fire what remained of the taste is exhaled, the smell evaporates, the colour alters, the figure is destroyed, the size increases, it becomes liquid, it heats, scarcely can one handle it, and when one strikes it, no sound is emitted. Does the same wax remain after this change? We must confess that it remains; none would judge otherwise. What then did I know so distinctly in this piece of wax? It could certainly be nothing of all that the senses brought to my notice, since all these things which fall under taste, smell, sight, touch, and hearing, are found to be changed, and yet the same wax remains.
Perhaps it was what I now think, viz. that this wax was not that sweetness of honey, nor that agreeable scent of flowers, nor that particular whiteness, nor that figure, nor that sound, but simply a body which a little while before appeared to me as perceptible under these forms, and which is now perceptible under others. But what, precisely, is it that I imagine when I form such conceptions? Let us attentively consider this, and, abstracting from all that does not belong to the wax, let us see what remains. Certainly nothing remains excepting a certain extended thing which is flexible and movable.
— René Descartes, 1911 edition of The Philosophical Works of Descartes (Cambridge University Press), translated by Elizabeth S. Haldane
Note the last sentence there and the insistence upon certainty. I can't say I agree with his assessment or argument, but it fits into his doubting of direct perception in order to advance the conclusions of his substance dualism. Certainty is, after all, only a mood.
What I hold fast to is not one proposition but a nest of propositions.
I am sitting with a philosopher in the garden; he says again and again "I know that that's a tree", pointing to a tree that is near us. Someone else arrives and hears this, and I tell them: "This fellow isn't insane. We are only doing philosophy."
-Ludwig Wittgenstein, "On Certainty"