This deliberate misuse of the word “deterrent” stopped being clever and/or cute decades ago.
In the modern world we have prisons, and the data suggests that the threat of decades in prison is at least as good a deterrent to the most serious crimes as the death penalty is. Think of all the mass shooters who turn the gun on themselves in the end; Why? If every perp thinks death is clearly the worst thing that could happen, then we should never see mass shooters / terrorists kill themselves after committing their crimes in a state (or a country) without the death penalty.