1
general::
Ease or assuage, make less severe, as in That snack took the edge off our hunger, or Her kind manner took the edge off her refusal. This term alludes to blunting the edge of a cutting instrument. Shakespeare used it figuratively in The Tempest (4:1): "To take away the edge of that day's celebration." The precise wording of the idiom dates from the first half of the 1900s.
American Heritage Idioms
2
general::
Phrase(s): take the edge off ((of) something)
1. Lit. to dull a blade. (Of is usually retained before pronouns.) • Cutting hard stuff like that will take the edge off your knife blade. 2. Fig. to decrease the effect of something; to make something less blunt, critical, etc. (Of is usually retained before pronouns.) • He did not mean to insult the guest, and he quickly thought of something to say that would take the edge off his remark. • Her comments were quite cruel, and nothing could be said to take the edge off of them.
McGrawhill's American Idioms And Phrasal Verbs