Permute rhymes with:
commute, mute, acute, bute, butte, commute, compute, cute, dispute, disrepute, impute, mute, nute, pute, refute, repute, subacute
Permute sounds like:
papermate, paramount, paranoid, parent, parente, parenteau, parenthood, parenti, parrent, peppermint, permanent, permanente, permeate, permeated, permenante, permit, permitted, permount, permut, permutate, permutated, pernod, preeminent, preened, premeditate, premeditated, primate, primed, print, printed, printout, printy, promenade, prominent, promote, promoted, pronto, prowant, pruned, pruneda, prunty, prurient, pyramid