Your cards play several times because you are fighting against the clown and their power is bugged to affect both players.
There seem to be more bugs at play here, but enemy clown starting effect is definitely one of the culprits. I managed to play the Polyrhythm 3 times in a single fight without any "exhume" effects. Other bugs would include the Groovy starter effect triggering on enemies and enemies exhausting your own cards.