1.
If you cut something up, you cut it into several pieces.
He sits in his apartment cutting up magazines...
Halve the tomatoes, then cut them up coarsely.
PHRASAL VERB: V P n (not pron), V n P
see also ~
2.
If one driver cuts another driver up, the first driver goes too close in front of the second one, for example after passing them.
They were crossing from lane to lane, cutting everyone up.
PHRASAL VERB: V n P