Mechanical means of controlling blackberries includes pruning the arching branches, digging up the roots or any other means where one physically damages the plant to reduce extra growth. If the mechanical control is too harsh, the plant will die. However, the arching canes often root where they touch the ground -- and even though you might cut the cane, new growth might emerge from the roots.
Herbicides are an effective way to control large areas of vines. The vines are notoriously woody with very tough thorns. After a few years, they can form a thicket that is nearly impenetrable with normal homeowner's tools. Herbicides sprayed on the leaves will slowly kill the plant, but they will also kill other vegetation in the area. Using chemicals for controlling blackberry bushes is more appropriate for destroying plants in an area instead of limiting their growth.
Mowing is a convenient way of stopping the spread of the blackberry bushes. Even though there might still be new growth underground, repeated mowing will stop the spread of any new shoots. Gardeners use this method to hold their blackberry hedges within boundaries.
Timing is important when dealing with blackberry control. Use the wintertime when the plant is dormant to mow over a blackberry patch that has overgrown its boundaries. You might miss a season of berries since the fruit is borne on last year's wood. The fall is the best time to use an herbicide since the chemicals need to travel with the plant's sugars down to the roots to effectively kill the blackberry bush.