Pull gently on the sucker to raise it from the ground. Use a spade to loosen the soil if needed so you can pull the sucker without breaking it.
Trace the sucker back to the main trunk of the vine. Suckers grow from an underground bud or nodule on the trunk of the main vine.
Use sharp pruning shears to cut the sucker from the main grapevine at the node or bud where the sucker originates.
Replace any soil that you removed to access the sucker.