Removed cactus spines do not grow back. If a pup is removed, another does not grow from the same aerole. Removing all the aeroles would stop the plant from vegetative reproduction, stop flowers from forming, and prevent spines from appearing. Typically, an aerole blooms one season then stops flowering. In a few species, they last more than one season.

That said, nothing stops a cactus from growing. If you damage the apex of a solitary plant, it is not rare for them to pup from a dormant aerole on the side, or a new plant forms from an apparently undamaged apical aerole. This leads to plants that look stacked.

An undamaged or dormant aerole sending forth a new shoot is best illustrated by the "Moon Cactus". When the Gymno. dies, the Hylocereus stock sometimes sits for a year or so. Often times, a new aerole develops (or an old dormant one awakens) that sends forth a shoot.

Thanks @Dzitmoidonc !
The main reason I was asking is because of grafting.I experimented with grafting with cactus plants I have.I've grafted rhipsalis cereuscula onto Austrocylindropuntia subulata.I know that the best rootstocks are from hylocereus,cereus and others,but I worked with what I have.Since A.Subulata pups like crazy,not much nutrients go into scion,but if I pluck out pups as soon as they appear,then eventually all the plant resources will go into scion,right? Also I have some cilyndriopuntia subulata that I used as rootstock with not much success.This cactus has a lot of long spines that makes it hard to work with it,so I wanted to pluck the spines out to make it easier to handle,but I didn't know will the plant just grow new ones,which would be a waste of plant resources and slow it's growth overall...