Thanks Muni for putting it into context. As you point out there are two aspects to the mind of enlightenment.
5heaps, not sure how to approach this because it is really rooted in Madhyamika philosophy which not everybody is into.
But if you do understand that Bodhicitta is the
mind of enlightenment (which I hope by now is established) then you should be able to see that mind is an existing phenomena - yes, it is shunya/empty, but nevertheless existing. There is no contradiction, for what anything is empty (shunya) of is independent/inherent existence of its own. Existence isn't being denied, it's the "independent" mode that is being refuted. This is basic Middle Way philosophy, albeit somewhat reduced.
What mind is, is the capacity to cognize/comprehend/apprehend - whether it does this conceptually or not. It can do this because it can interact, change etc (in fact it never stops doing so for an instant). Alias it does not have a fixed, independent mode of existence.
If one were to follow your logic:
how can bodhicitta be both a 'mind of enlightenment' and the lack of inherent existence? the first is a positive phenomena the other a negative phenomena. one object can't be both, since they're a dichotomy.
it would contradict the Buddha's most basic teaching that is dependent arising, which thankfully He taught. Nagarjuna explained quite thoroughly that dependent arising and emptiness are two sides to the same coin. He and others praised effusively the Buddha for teaching dependent arising.