This does not make sense. If you are licensed, and if you kill everything--you will have bare soil--and that invites new weed seeds--not to mention soil erosion, mud and dust due to wind. Tall brush and vines cannot withstand mowing. Area needs to be planted in a grass suitable to your area and mowed regularly. Bermuda, right?
Otherwise, weeds will return. Vines should be cut off at the soil level--everything above the cut will die. Then start to cut--never letting the vines get over 2 inches tall.