The Pirates of the Caribbean actor - who has 9-year-old son Flynn with ex-wife Miranda Kerr - adopted the pup in 2017.
Mighty's disappearance comes just months after Katy lost her cat, Kitty Purry.
The singer paid tribute to her late pet, as she thanked her for "the cuddles and companionship along the way".
She wrote on Instagram in April: "Kitty Purry crawled through my then-boyfriend's window 15 years ago, fully pregnant and seeking shelter. Two litters and many moons later, this street cat became a lovable mascot to many. Sadly, Kitty completed her 9th life last night.
"I hope she rests in salmon fillets and tuna tartare way up in catnip heaven. Kitty, thanks for the cuddles and companionship along the way. Big thanks to my brother David and @garethwalters for being great co-parents ... #kittypurryforever (sic)".
Animal-lover Katy also has a dog called Nugget, which looks just like Mighty.
And two years ago, Perry almost lost the teacup poodle after it jumped off her bed and was unresponsive for three minutes.
Luckily, the 35-year-old singer's assistant saved the canine's life when she performed CPR on the tiny dog and managed to bring her back from the brink.
In a video shared by the singer, Tamra said at the time: "I pushed on her little chest and I blew in her mouth and I brought her back to life."