I have never encountered countable execution (that is, executions or an execution) except in the sense of an instance of executing the order of a court of law (including an execution of the death penalty); and the only other uses reported by OED 1 are of a sense obsolete since the early 18th century: “a performance” of an operation, work or piece of music.
1628 Look to your actions, to your doings, to your executions and performances.
OED gives no citation of this with executions or an execution as object of a verb.
What you do still encounter from time to time is do execution, used originally of military actions with the sense "inflict destructive effect"
...an adder, when she doth unroll
To do some fatal execution —Shakespeare, TitA
This has been later extended in a figurative (and I think largely jocular) sense to “the effect of arguments, personal charms, etc.”
Black eyes, which might have done some execution had they been placed in a smoother face. —Thackeray
One might, I suppose, speak of “an” execution, in the sense of a performer’s manner or excellence of performance on some particular occasion—
Sartorius gave us the A-minor with a polish and an execution far above his usual mediocrity of expression.
but that sort of execution is not done or performed, it is a quality of the performance.