Unwrap vines from around the flowers. Use your finger tips to gently tease the vines off the flowers without causing damage.
Cut the vine into sections if it is wrapped tightly around the flowering plant, and remove all sections from the garden bed.
Trace the vine down to the soil. Dig under the soil and lift out as much of the root system as possible with a garden fork. Many perennial weedy vines regrow from small sections of roots left in the soil.
Remove all flowers and seed heads before the seeds disperse. For annual vines, removing the seed pods is often enough to eliminate the vines. For perennials, reducing the amount of seeds helps to keep new plants from growing but doesn't stop the spreading root system.
Place vines in the garbage or city refuse container. If you put them on the compost heap, the vines will likely return everywhere you spread the compost.
Mulch the flower bed after you remove all the vines. Spread straw, pine bark, sawdust, leaf mold or a similar organic material six inches deep around the flowers and established plants. The mulch suppresses some weed growth and seed germination.
Pull out vines as soon as they appear. Methodically pulling out vines before they flower will slow or eliminate them in a flower garden.