Blue Heeler problems?

I am having trouble with my dog. He's a Blue Heeler Beagle cross and he's been neutered and will be three this November. He is a very sweet dog but is too smart for his own good! He is in a fence for most of the day with two other dogs, both female, but he always finds new ways too get out and when he does he gets into trouble! He's dug under the fence, gone through the fence he can even jump over it! When he gets out he runs around and scares the birds and rolls in things or if the cats or nabour's dog is around he chases them! The nabour's dog has had to be taken to the vet twice because of my dog and is threatening to shoot on sight! My dog has attacked our cats many times but over the last few weeks things have steadily grown worse. He recently caught one of our cats back legs while chasing him and nearly disabled him! The strange thing is he didn't break the skin when he attacked our cat. He has done all of this when i'm either at school or on vacation so i think it might have to do with my absence. Also the nabour's dog taunts our dog so that is probably part of the reason. Any advise would be greatly appreciated!