When you trim a voice memo in the Voice Memos app on your iPhone, you get two options to save the trimmed file. The first option says Trim Original. What this option basically does is it trims your actual voice memo and overwrites it on your phone;
If you choose the second option which says Save As New Recording, then your trimmed memo is saved as a completely new memo on your iPhone. This does not overwrite your original memo and it gets preserved on your phone..