Cut To leave or depart. (aka: "cut out")
Ex: Let's "cut out".
To outdo another person
Ex: Charlie's solo really "cut" that cat last night.
A battle of the bands.
Ex: Basie and Lunceford's band had a real
'cuttin'contest' last night.
Black musicians used to get together for a Jam Session and "Chop Heads".
This term referred to the ability to take a solo on the same instrument and "chop the other guy's head off" with your abilities.
Of course, "Cut" is synonymous.
"Head Choppin'" is the act of following someone's solo with a solo so profound that the poor cat who took the first solo must tuck tail and slink away.
This one likely points back to the "Cakewalk" of a time previous, BTW.