One of the few herbicides that will work on mature spurge is glyphosate (Round-Up). But be careful, as glyphosate will kill anything it comes in contact with. Even with this, the spurge may still regrow from the roots so check frequently for regrowth and treat the plant as soon as possible if you see it.
What herbicide kills spotted spurge?
2. Controlling an infestation of spotted spurge. If you've got a large spotted spurge problem in the lawn, apply Ortho® WeedClear™ Lawn Weed Killer Ready-to-Spray or Ortho® WeedClear™ Lawn Weed Killer Concentrate according to label directions.
What kills spotted spurge?
Small patches of spotted spurge plants can also be killed using a read-to-use lawn weed killer, like Scotts® Spot Weed Control for Lawns. Be sure to follow label directions and only use on listed grass types.