Apple sauce pronounced in Japanese style is "appuru sauce". You can say it in English and people will understand - at least people will guess you are talking about some kind of sauce made of apple. The problem is that apple sauce is not so common here, you can find apple jam instead, but jam is usually not puree but chunks.
I made applesauce, and good sauce at that, for my first try. My wife found it weird, and probably as tasty as the average foreigner finds kochi the first time around. Apple jelly is fine and good, but apple sauce is weird.
Pronunciation is simply apple sauce in a heavy Japanese accent (i.e. katakana).