Green’s Dictionary of Slang

to overtake another vehicle by driving recklessly in front of it (and forcing it to take some form of evasive action).

1821		‘An Amateur’ Real Life in London I 341: The pride of becoming an accomplished whip — to know how to turn a corner in style — tickle Snarler in the ear — cut up the yelper — take out a fly’s eye in bang-up twig.
1997		N. Barlay Curvy Lovebox 87: Leery van drivers everywhere. One of them cuts me up so I give him some horn.
1999		Observer Escape 17 Oct. 3: BMWs are cut up mercilessly by buses from rival companies racing each other.
2000		Guardian G2 7 Feb. 11: A man cut me up really dangerously coming off a slip road.
2009		L. McIlvanney All the Colours 123: [He] gave the finger out the window to a minicab that cut us up.