The UK had the same problem when they banned pit bulls. Not a single dog was killed. They just disallowed people from getting new dogs, and the ones that already existed just died out of old age in their existing homes. If new dogs are found they just go to an animal shelter where they get neutered and that's it.
In some cases, like the US, unwanted (but legal) dogs go to Canada where they get new homes. Checkout YouTube for that, they all look like happy puppies.
Not a single breed-specific-legislation in the world resulted in any dogs getting killed.
What we're talking about here, is dog breed which single handedly are responsible for over 90% of fatalities and serious injuries should be neutered and not allowed to be sold to the general public. They can be in shelters, as guard dogs or used by the police or military, just not regular family homes with elderly and children who can't defend themselves.
Where did you get that gruesome idea of killing dogs from?! No one anywhere in the world has done that or even talked about it.
What do you do with them? Further, if it's illegal for anyone to buy them, what do you do with them?