Ask Mr. Smarty Plants

While we hate to recommend herbicides, you are correct that a small piece of root will generate fresh agaves, just what you don't want right now. We know you don't want to hear this, but digging them out with a good sharp shovel is the best way to begin. And disposing of them is going to be tough, too. Please don't put them in the compost pile, those thorns can last forever. A long-handled shovel, long heavy leather gloves and maybe heavy pruners to kind of cut the job down to size are going to be necessary. The best suggestion for cutting them down and keeping them down that we have found so far is to get some glyphosate herbicide and a few disposable sponge brushes. Don't go wild with this, because you want that area to be hospitable to your new landscape, so no spraying or drenching the soil. When you have removed all the root you can by manual (as in labor) techniques, make a clean slice across the remaining root and, within 5 minutes, paint that open wound with the glyphosate, full strength. You have to do it right away, because the agave, like all other survivors, will quickly move in to heal that cut over before the herbicide can get to the rest of the root. You will still get pups popping up over time, and waiting a while before you put in the raised beds is a good idea.

And, lesson for the future: When the pups pop, get them out while they're little. Get it all out with the same sharp shovel if you can, and do the paint job on any root remaining.