Dumpster Gang how to escape the Exterminator comes down to one move: stun John, then keep moving before he gets back up. What happens after that depends on whether you are alone or with a crew.
Dumpster Gang how to escape the exterminator when caught
If John grabs a raccoon, that raccoon is put in a cage. How bad that is depends on who you are playing with.
Playing solo, a caught raccoon can get out of John's hands on its own, so being caught is an inconvenience rather than a failed run. In co-op the raccoon stays in the cage until a teammate opens it, which is why a group that gets caught has to split the work. The teammate rescue guide covers that side of it, including the demo bug that makes the rescue itself dangerous.
The stun-and-run loop
Any throwable object or a melee weapon that connects with John stuns him, and you can run off while he is down. That is the whole escape: stun, move, keep moving. It is also the same move that solves the house mission's coffee objective, which is why the pick up and throw guide matters more here than anywhere else.
Cover after you break away
Getting into cover afterwards keeps him from picking you up again. The good spots are the small space under the stairs, a bush, and a hiding box such as the laundry basket or the crate.
The difference between a stun and an escape is whether you end the stun somewhere John cannot immediately grab you again. The stealth guide covers where those hiding places are on each map and what gives you away while you use them.