Kill dinos, destroy rafts, move dinos off server. That's about it sadly.
Just gotta wait for the smaller tribes to move to a new server where they can tame - we've had people on our server complaining that they only have 20 dinos and us bigger tribes should kill some of ours so they can tame more. Right, I'm gonna kill my bred rexes so you can tame a lvl 20 parasaur lol. But yeah, eventually they'll realise the server is full and they'll look for a new home and things will ease up. It happened on Legacy, it'll happen again lol