Probably the best way is to just not let your dog be around cats.

Keep him on a leash when he's outside.

well, for one keep him in doors or in your backyard away from cats. You could try punishment techniques such as a small whack on the nsoe with a newspaper or even a shock collar when he shows aggressive behavior towards cats to train him not to. but it's up to you if you want to put your dog through that

Oh my! Well if I was you I would put a shock collar on Fido. If he's actually hunting and murdering my feline friends and he's not contained it would be wise to invest into some alternative methods of containment. http://www.hitecpet.com/

You cannot cure your dog of this kind of behaviour, you can only prevent him from being able to hunt cats. Keep him aways from cats and keep cats away from him. A high fence around your yard can help. Also by wearing a muzzle you can limit the damage done to the cat.

Some breeds have a much higher prey drive than others, even with mixed breed dogs. It is unlikely that you will be successful in stopping your dog from this behavior. I would plan on not allowing the dog access to cats as my first line of defense. You CAN TRY to work on supporting him in being less reactive to cats. But, you need to insure the safety of the cat/s while exposing him to them. Typically, dog on lead, and you able to control the dog (a halti or gentle leader head harness is best NOT A CHOKE or Pinch coller) Cat is allowed to be seen by the dog at a distance...you ask the dog to sit/stay and reward the dog for doing so, as long as the dog IS NOT reacting to the sight of the cat you continue to reward him...little bits of human jerky (plain) are great..your reward needs to be MORE INTERESTING THAN THE CAT. Over time, still on lead and under your control, the Cat can be allowed closer in the same room. As long as the dog is NOT responding he earns his treats EVERY TIME he sees the Cat. Anytime the dog responds by leaping up, barking, whining, or straining to get loose..the "GAME" training, rewards STOP, and you remove the dog or cat from the room. Don't bother thinking that saying "bad dog" will get him on board..your goal is to reset his desire for the cat with desire for positive things of a different nature...treats/special toy/praise from you. Teaching him to be 100% reliable on his COME/Sit/Down (laying down) and STAY are your best support behaviors. However, I would still NOT risk a Cat to prove that he's good to go, nor would I plan to leave any cat with this dog alone EVER.

I would keep him contained in a fenced yard, for when you are not around. I hate to say this, but if he has the tendency to attack smaller animals, he may eventually bite a person. Please make sure he is kept on your property, our friend lost his dog, to euthenization, because he went out of the yard, and killed his neighbors cats, since it was so vicious, they put him to sleep (animal authorities). Good luck to you, and your pet.

even a dumb man can answer that, "MOZZLE THE DOG"!!!!!!!!!!!!!!!!