There's another interpretation of this "casting time" conundrum. The cantrip replaces one of your attacks, but nowhere does it say that the casting time changes.
Round 1
Player: I make one attack with my rapier, and use my other attack to cast mending.
DM: Remember, mending has a casting time of one minute.
Player: Yep, that's right.
Round 2
Player: Okay, I make two attacks with my rapier.
DM: Remember, you're still casting mending. Do you wish to abandon that spell?
Player: Shoot, I forgot. I'll make one attack, and use my other attack to continue casting mending.