I planted some mazus reptans last year, and it did well, filling in the area I needed. After a cold Utah mountain winter and a ton of snow, it has a thick mat of brown, dead stuff. The new growth is coming, under all the dead stuff. Should I rake away last years' growth, or just be patient and let the new growth come up through it?
Yes, you should prune any dead or damaged parts of the plants.
Gently raking can remove some of the dead material but you should use caution not to dislodge the root sytem.
Trimming by hand may be necessary for a good clean up of the ground cover.