A few years ago, my mother had her notary draw up a mandate for future protection and appointed me as proxy. I've accepted this responsibility, but I'd like to give it up. Is this possible?

Yes, but under certain conditions. As long as the mandate has not taken effect, you can renounce your status as mandatary (art. 489 al. 2 C. civ. and 492 al. 3 C. civ.). You must notify your decision to your mother, the mandator, by registered letter with acknowledgement of receipt, and to the notary (art. 489 al. 2 C. civ..).
 

On the other hand, once this mandate has been implemented, renunciation is no longer possible.