English Translation
The mouth is the executioner and the doctor of the body.
This English proverb is really hard to translate in Japanese in a natural way. But I can firmly say, at least, that 体の死刑執行人 sounds very unnatural in Japanese. My alternative free translations are:
食事は毒にも薬にもなる。（しょくじはどくにもくすりにもなる）= (lit.) Meals can play a role as poison as well as medicine.
医食同源（いしょくどうげん）= (lit.) Medical treatment and meals have the same origin.
毒にも薬にもならない is a frequent idiom, meaning “it’s neither poisonous nor useful” (i.e. useless but not harmful). So, 食事は毒にも薬にもなる may also sound natural to native ears, I think.
医食同源 is a common idiom. People say 医食同源 when they want to give an advice on healthy meals. 医食同源 is probably close to the essence of “An apple a day keeps the doctor away” in English.
I don’t like 口 as a translation in this context. We usually use 口 metaphorically to mean “speaking”, not “eating/food”. – For example, 口は禍の元（くちはわざわいのもと）means “Out of the mouth comes evil” or “First think, and then speak”.