I assume you'd be more interested in the murder rate than the number of actual murders. But it's difficult to tell, at least partly because the way the data has been gathered has changed over the years. Being up-front, there does appear to have been an overall rise since the mid 1960s, but I think you'd be hard-pressed to show a causal link.
And, besides, the simple point is that the death penalty isn't really about deterrent. No amount of harsh punishment will stop "spur-of-the-moment" crimes, or crimes of people who had no regard for their life anyway. How many mass school shootings in the US end with the death of the perpetrator on the scene? Too late, as they've already done the damage, but death was no deterrent to them. And, as I said before on this thread, history proves that the death penalty is wholly ineffective as a deterrent no matter the crime.