Iggy Azalea -- My A$AP Rocky Tattoo Has Gotta Go, ASAP!!!

Nothing says you're 100% done with an ex like a laser burning his name away -- just ask Iggy Azalea ... who's finally getting her A$AP Rocky tattoo removed.

The "Fancy" singer went to the Beverly Hills office of tattoo removal king, Dr. Tattoff on Tuesday -- and walked out with a bandage on her left pinky ... where A$AP's name once lived.

Iggy got the tatt years ago when they were dating. When they split, she just had his name crossed out ... but now she's making a permanent change.

Finally ... room for some fresh Nick Young ink.