If the DQ was behavior-related (drug use, etc), then the rider is DQ'ed for the whole event. In the case of missing a gate, the other run would stand. You may have to elaborate on your situation regarding SS if this did not answer your question. Thanks!
I'm not sure how missing a gate equates to a slopestyle dQ, but let's say for example the kid does a solid first run, but then does a backflip on the second run - in a comp where inverts are forbidden.