Captain Jack Sparrow got carried away with the smuggling -- Johnny Depp's 2 Yorkshire Terrier pups have a death sentence hanging over their heads because Depp allegedly snuck them into Australia.
Australian officials say Johnny and Amber Heard failed to declare Boo and Pistol when they arrived on a private jet last month. Under Australian law the dogs are supposed to be quarantined for a minimum of 10 days ... just to make sure they're not carrying any foreign diseases into the fragile ecosystem.
If Johnny, or more accurately ... Boo and Pistol don't hightail it out of Oz by Saturday -- the country's Agriculture minister says they will be put down.
A rep for Johnny -- who's down there shooting the 5th 'Pirates' flick -- told the AP the dogs are under a "home quarantine" ... but wasn't more specific than that.
Pretty harrrrsh sentence ... but Aussie officials say the law is the law.