Absolutely idiotic.
Think about it: 10 years from now, the irresponsible owners won't own mutts - there won't be any left in the state. The irresponsible owners will own purebreds. The purebreds don't have to be sterilized. The purebreds will run off and breed with the neighbors purebred.
Then again, this bill will also make it unaffordable for many families to even own a dog. There's a big price difference between being able to go adopt a dog from the SPCA for $50, and having to shell out $500 for a purebred. Plus, as they eliminate mixed breeds from the state, the demand for purebreds is going to go up (higher demand -> increased price.)