Vinca minor (common name perwinkle) is a perennial groundcover native to Europe and introduced to North America in 1700s. Vinca spreads vigorously and can become invasive, displacing native species. Because it is so hardy, vinca can be difficult to totally eradicate from your landscape, but it's possible.
Use a hedge trimmer, mower or weed trimmer to cut the vinca as short as possible.
Dig up the area where the vinca is growing. Vinca has long, tenacious roots and runners, so dig up an area at least 36 inches wider than the plant's location.
Pull out all the vinca pieces and place into the trash. Do not compost any part of it.
Spray an herbicide containing glyphosate (such as Roundup) on any vinca that reappears. You may need to use multiple applications, and the best time to apply is in the warm months when vinca is actively growing. Use care when applying, because glyphosate will kill any broadleaf plants and grasses that it touches, according to the University of Minnesota Extension.
Wait two to three weeks for the herbicide to kill the remaining vinca, then dig up and dispose of all the pieces.