Roundup is okay,(the industrial stuff) You need a card in my state to buy it. There is some other herbicides that are better for woody species that will work better. Be careful of water run off. If you really want to kill the multiflora rose, mix roundup with diesal fuel as the surfactant, then come along and bush hog it.
Another option is to rent a skid steer with a bush hog and only cut sections in order to get the deer to move where you want them. They will take the easiest route. I agree with the other guys, if burning is not an option. If you spray then burn would be the best option in my opinion.