Other than using a backhoe, there is no other way to remove them out of the ground. You can apply a systemic weedkiller to kill the roots. These travel throughout the plant's system to the roots. Two that are often used are roundup and vine-x. These will work best when applied at a time when the soil will be dry. Be careful not to get any drops on plants you wish to keep. Websites for these weedkillers are below.