Green’s Dictionary of Slang

stomp v.

also stomp in, stomp on, stomp out
[SE stamp/SAmE stomp]

1. [1940s+] (US) to beat up, to defeat.

2. [1950s] (US teen) to dance.

3. [1980s] (US black) to use language that is likely to cause a fight.

In compounds

stomp-ass (adj.) [-ass sfx]

[1940s+] (US) violent, aggressive.

In phrases

stomp it (v.) [one ‘stomps’ on the accelerator]

[1930s] to hurry, to go fast, esp. in a vehicle.