I was wondering if BLS-Envoy's removal effect destroys the targeted monster and removes it from play, or just removes it from play without destroying it? Also, can My Body as a Shield be used to save the targeted monster from BLS-Envoy's effect?
Thanks in advance.

No because Envoy simply removes the monster and does not destroy it. If something destroys it and removes it, it'll say so.

nope--if you read BLS's text, it only says "remove the selected monster," not destroy, so MBAAS won't affect it.