Cut down Algerian ivy to the ground using a pair of garden clippers. If the ivy is growing in a tree or on another structure, cut it down rather than yanking it down. If it's stuck to the surface, gently pull off the aerial rootlets to minimize damage. Afterward, hand-pull or use a spade to remove as much of the roots as you can from the ground. Be careful not to remove the tree or other plant roots when removing the ivy roots.
Mow low-growing Algerian ivy with a lawn mower set to a 2- or 3-inch height. Alternatively, cut Algerian ivy down as described in Step 1. Then, apply glyphosate to the foliage that is still attached to the roots. Use a ready-to-use glyphosate solution, if desired, that has a built in applicator and does not need to be diluted with water. Use the herbicide as indicated on the label, and wear protective clothing and gloves to avoid contact with the chemical.
Mow or cut down Algerian ivy whenever it grows instead of using glyphosate or digging out the roots. With persistence, the roots will starve to death from lack of sunlight.