The term comes from the hammer action on a gun. The hammer dropping on many pistols is what causes them to fire. If you "drop the hammer" on somebody, you go all out.
The expression can be used in several different variations with the above definition: 1) ...part. in a draconian way 2) ...leaving a wake of destruction in its path 3) ...against a very specific target with precision; etc.
"You have the green light. Drop the hammer on that motherfucker."
BANG. Bad guy fall down.