On Heels of His Mom's Death

4:40 PM PT -- Johnny has filed his response through his lawyer, Laura Wasser. He is asking the judge to reject Amber's claim for spousal support.

And we know what you're thinking ... they have NOT decided what to do with their pooches, Pistol and Boo.

Amber Heard has filed for divorce from Johnny Depp ... shockingly 3 days after Johnny's mom died.

Amber filed her

Monday, citing irreconcilable differences. The couple married in February of last year, yet Amber is asking for spousal support.

Our sources say the couple had NO prenup.

It's especially harsh because Johnny was extremely close to his mother. She says in the divorce docs that they separated on May 22 ... 2 days after Johnny's mom passed.

As if that's not enough ... Johnny's new movie, "Alice Through the Looking Glass," opens Friday.