Managing Sweet Potato for Propagation

Hi,

I'm new to sweet potatoes. What is the best way to manage a sweet potato plant with the main purpose of producing a large number of slips? I was given a rooted slip a few months ago and it has grown into a vine crawling over my mulch. I don't think I'll hurt it at this point.

Should I be burying the new growth? Or waiting for tubers and then harvesting them? Or clipping and rooting the new growth?

Thank you for your time,
Daniel