What's a good way to remove invasive plants?

Update: I have plants growing that I can't even dig out, the roots are deep. The plants come from Birds burying seeds. Any ideas about how to kill them, preferably no herbicides.
Update 2: My yard is a large, fully mature with lots of ground cover around the perimeter. In the ground cover I have lots of new trees popping up like oak, Chinese pistachio and such and I have enough trees, don't need any more. I have a dog and would prefer not to use anything poisonous. I know I should have done... show more My yard is a large, fully mature with lots of ground cover around the perimeter. In the ground cover I have lots of new trees popping up like oak, Chinese pistachio and such and I have enough trees, don't need any more. I have a dog and would prefer not to use anything poisonous. I know I should have done something when they were real small. some are about 4 feet tall.
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