Mulches will help control Spurge, and many other "weeds", but it will not necessarily eliminate it. Spurge, like many other similar plants, will root from tiny bits and pieces of the plant left behind, so pulling it and making sure all of it is removed from the planting is the single most bestest way of getting it out of the garden. Spurge also seeds quite prolifically.
I have, manhy times, covered this with newspaper and a mulch and let it die so the nutrients it removed from the soil were put back. but it does grow in the mulches I put down too.

Another problem is tat many seeds are lying in wait for the correct conditions to germinate. It's called the Soil Seed Bank.

Nancy, with spurge and with the stinking little violets, I will sometimes save cardboard boxes and fit them arount the plant then mulch on top of the cardboard...takea a little while, but gives me lonnger weedfree time than anything else I've tried.
kay