* Δίωξις (díōxis): This word means "pursuit" or "prosecution," and could be used metaphorically for someone who pursues and carries out a death sentence. It's not a direct translation but hints at the action.
* Θανατωρός (thanatōrós): This word means "death-bringer" or "killer." While not specific to an official executioner, it describes the function.
* A combination of words: You might need a descriptive phrase, such as ὁ τὸν θάνατον ἐπιτελῶν (ho ton thanaton epitelōn), meaning "he who carries out the death" or something similar. This would depend on the grammatical context and you might have to adjust the pronouns.
The best choice depends heavily on the context. If you can provide more details about the situation in which you'd use the word, a more precise translation could be suggested.