How close to the trunk are they? If there are a foot or more I would use a sharp spade to sever the connection to the main tree and then leave it a lone for a few months and let the now independent tree grow some more roots before digging it out and transplanting late winter/early spring. I'm assuming your tree is grafted and what you'll get is another rootstock ready to be grafted.

My take: Many woody plant species have dormant buds in stem and or root tissues, at or below soil surface. Frequently, the highest density of these buds is found at the root collar (or basal flare), but many species contain these buds in roots near the surface. In a normally growing tree, the hormones auxin and cytokinin have something of an antagonistic relationship, with the auxin stimulating apical growth and suppressing cytokinin's stimulation of lateral or secondary (to apical) meristems. Without getting too complicated here by getting into branching index, it should suffice to say that anything suppressing the flow of auxin will normally stimulate dormant buds. Since auxin is produced in apical meristems and leaves, tree injury (including pruning) that reduces auxin production and its suppression of dormant buds allows cytokinin induced activation of the buds. Of course, we would look first to pruning, especially improper (as in tip pruning) or heavy pruning as causal. A few other causes might be insects, wind damage, disease pathogens, cold injury, etc. Al

Hi Bill - I don't know that the tree would be weakened exactly, if you left them, though I might wonder if it would divert the tree's energies from fruit production to vegetative expansion, so limiting the suckers is probably a wise idea. Any chance you could lift a number of them with roots attached, start new plants and then find homes for them? (you might have a mini-business literally growing under your feet!) Maybe someone else will add their thoughts about whether black plastic laid down would be okay or detrimental to the tree's ability to get oxygen, moisture, nutrients, etc. Is this an area where you could simply use a weed whacker or whatever, to spare your back from hand pulling? some of us would love to have your problem, believe me (a mature Black Mission fig going gang-busters). Hope you get more input, I'm no expert, just grow figs in containers and only a few send up suckers within their pots, so it's not been a problem I've encountered personally on the scale you have. Sherry

Air-layering is the safest way to root that branch. It should have hardened wood in center in order to strip down a inch of bark from it, and from your picture is to early for this.