I recently cleared a number of large bushes and hedging in my garden. I was left with a huge amount of branches to dispose of. Normally for small amounts I would bring this to our local recycle center in a trailer but this would have meant a number of trips. Instead I got a loan of a chipper machine from a friend and chipped all the branches and leaves and spread the resulting mulch around the larger established plants in the flower beds. It was so much easier than piling everything onto a trailer, I highly recommend it.
One thing to be careful about though, is to make sure that none of your plants carry disease. As chipping these plants and spreading it around may simply infect all the remaining plants in the garden. If you suspect this is the case perhaps the best solution would be to dry the chips and use them as a fuel in your stove/ fire or dispose of them separately. Also it is better to simply leave the mulch on top of the soil instead of mixing it with the soil. The mulch helps to retain moisture in the soil, prevents leeching of soil nutrients after heavy rainfall but importantly as the mulch decays it uses nitrogen and if mixed in with the soil it will deplete this and thus harm the growth of adjacent plants.