Autumn Olives are not that difficult to kill, but impossible to eradicate in my opinion. Mechanical means such as digging or pulling out is probably best where applicable. Several chemicals will also kill it, some through foliar treatments, but the most effective is applying the chemical to the cut stump immediately after cutting. Glyphosate/Roundup, Imazapyr/Arsenal AC, Triclopyr are a few known chemical controls for Autumn Olive.
This site has those chemicals listed with prices to give an idea of their uses and cost:
http://www.keystonepestsolutions.com/
Mowing/bushhogging might keep them under control and may even kill seedlings, but it will not always kill established shrubs. I know of a field that was not mowed for 6 years and the autumn olives became abundant. The same field, for the last 4 years has been mowed 2 times every year and the autumn olives are still living, waiting for their chance to take off.