Is it possible that repeatedly jabbing a cancerous tumor with a biopsy needle spread cancer cells from the tumor?

Yes: It is possible multiple needle biopsy spread the cancer cells.

I say "No": We've looked at this ever since I was on my third-year pathology rotation in med school 40 years ago. The findings keep coming back with the evidence of any effect conspicuously absent. If it were a mechanical effect, tumor would recur along needle tracks -- and it almost never does. I suspect cancer cells sneak into the bloodstream often, but can't spread until they've acquired the ability.