Will a rototiller cut up roots?

In general, no, a roto-tiller is not meant for cutting through roots. It is just meant for "fluffing up" soil that has become packed or hard.

My roto-tiller is a little electric push-type, and it won't cut anything bigger than grass roots. But it will "grind away" at larger root of flowers and bushes until they eventually give through. I usually get out the shovel or pick once I hit something like that.