The AI got a stupid city in the middle of no production, where there is some nice cave tiles with science. Can I just raze or relocate their cities?

ransack it

what you can ransack your own city? sounds insane

There is a solution just build a district near the tiles you want, or on top of them. Doing this lets the city work those tiles.

expect very certain districts (Harbor, Khmer's unique district, Helmet), districts only have one or two types of yields. In the early game, good city placements can yield huge science and quickly move you all the way to medieval where you unlock more flexible options for your cities.