Im not familiar with amiga games since I never owned one but the description you provided sounds like Midnight Resistance. It was an arcade game that was ported to home systems. I looked it up and saw there was an Amiga port.
Sounds like you are mixing up a couple of different games. There is D.D Crew which is an arcade game with the first level set in an amusement park. The other game I can think of is The Combatribes which was released in the arcade and was ported to the SNES. The second level is set in an amusement park and the enimies are clowns. You cant pick up any weapons though. Hopefully it is one of these games.