What to do when mounds of iceplant abound in the garden

Q. I have what I call iceplant since I don’t know what it actually is, which blooms beautifully in March and April. But it keeps growing in higher and higher mounds. When cutting it back on the edge, I see a lot of dead material. Will it continue to keep growing higher each year? Is there anything I should do? 

Iceplant could be seen everywhere in Southern California when we moved here in 1988. Native to South Africa, it is a fast-spreading succulent that tolerates poor soil and drought...