There are 2 sentences which are similar but mean quite different things in English.

1) "Don´t do it, because he says so."

This means: "Don´t do it! He says so!"

but there is also:

2) "Don´t do it because he says so."

This really means: "Don´t do it just because he orders you to do it."/"Don´t do it even though he says so".

It can also mean "Don´t do because he says so, but for some other reason. Do it because you want to ...."

How to translate the second sentence into Turkish?

O öyle diyor diye yapma.

Teşekkur ederim.

Is there perhaps another way to say it?

I agree with göküyüm.

To add emphasis you could also add sırf or sadece. i.e. don´t do it just because he says you should. (If that is the shade of meaning you wanted)

OK. Where exactly, within the sentence, would you put "sadece"?

at the beginning of the sentence.

By the way, I assume "don´t do it because he says so" means "don´t do it because he tells you to do it" , right? because in that case you can simply say "o diyor diye yapma". I think there is a nuance between this one and " o oyle diyor diye yapma" . The latter is more like "don´t do it because he thinks that way(or because of his opinion). But this is just hairsplitting anyway.They will both work fine. You can also say " o dedigi icin yapma" or elaborate the sentence with sadece or other words