You should cut them off. They are coming up from below the graft.

From my understanding that would be good rootstock. I would try and pile sawdust or compost around the base ofthe suckers and wait for then to root, cut off below roots, and graft your scion.. CAUTION: Do not pile soil/ mulch around the base of the big fruit Tree, it will lead to rot,etc. Just around the new suckers coming from the roots. Hope this helps

Joe

You want to cut the suckers off. They will take energy from the roots that otherwise would have gone into your grafted variety (Florida Sun). It's possible if you let the suckers go long enough, the tree could reject the graft altogether.

The peach is probably on some plum rootstock, as peach rootstocks almost never sucker.

Nurseries like suckering rootstocks because they are easy to propagate by stooling, as mentioned. However, they are a pain to me. Some you have to continually remove suckers.

Thank you. I will cut them off.

I'm not an expert/serious hobbyist or anything like so I won't be grafting anything on them. But if I rooted the suckers, would they be plum trees??

"But if I rooted the suckers, would they be plum trees??"

Assuming it's a plum rootstock (which it probably is) then yes any suckers that you could root would be identical to the rootstock (plum).