Untangle and cut the sweet pea vine from other plants and objects, if necessary. Leave enough of the stem so you have something to hold to pull them out.
Pull the sweet pea plants from the soil, roots and all. This process is often easier to do when the soil is moist. Pull up any additional sweet pea plants that later sprout.
Throw sweet pea plants that have flowered into your trash, not your compost pile. In the compost, the seeds may work their way back into the landscape.
Apply glyphosate to the foliage of your sweet pea plants as an alternative to hand pulling. The herbicide will work its way from the foliage to the roots, killing the sweet peas in the process. Use glyphosate carefully and according to the label instructions. Note that glyphosate will kill other plants and grass as well if they are exposed to the spray.