dédoceó is a very rare verb, but it is classical. I'm not sure, because I haven't been able to find all of the examples cited in L&S, but from what I have seen it means something like to 'unlearn' a thing. In this case I don't think it would capture the whole sense of 're-educate', which generally means 'remove someone's beliefs and add new ones' - you might have to use an expression like dédocére ac simul alia docére, 'un-teach and at the same time (simul) teach other things'.
However, it would be useful to know precisely what you mean by 're-educate'.
In addition, you might consider adding something to mente mentem to make it a bit clearer that you mean 'with my mind, [educating] someone else's mind': i.e. meá mente mentem.
In summary, my suggestion would read:
dá mihi potestátem meá mente mentem álterius dédocendí ac simul alia docendí. 'Give me the power of 'un-teaching' the mind of another with my mind and at the same time teaching them other things' (for want of a better word than 'un-teach' for dédocére).
Or with an ut clause: dá mihi potestátem ut meá mente mentem álterius dédocére ac simul alia docére possim. 'Give me the power so that I can 'un-teach' the mind of another with my mind and at the same time teach them other things'.
But I'm not altogether sure about it, particularly over whether docére/dédocére is appropriate here, so I would wait for other replies first.
In the Mage: The Awakening rule book the spell is named Psychic Reprogramming and it allows the spell caster to alter and/or delete any aspect of the subjects fundamental psychic makeup, such as turning a friendship into a rivalry, making the target fall out of (or into) love, or making him follow a new career calling. I hope this helps.