There has been handful discussions about How to fix a bolt on a climbing route. But there seldom any point made about How the one should go about when removing/replacing the bolts.
In the UK this is controlled/coordinated by the BMC.
They publish an extensive guide on how and when to do this Bolt Guidance Document.
There is also a working group, coordinator and they even pay for new bolts. There are lot's of issues around this, the document goes into a lot of detail these. The most important one (in the context of your question) is.....
When to replace bolts
(sic: Bolts do fail but not very often).....After all when was the last time you heard of a bolt failing? Well it does very occasionally happen and recorded cases suggest in some situations that are hard to predict. So what factors should we take into account?
Rock quality
Like any other form of protection, a bolt is only as good as the rock it is placed in.....Always remember that the erosion that creates our crags has not halted. The weather and particularly cliff vegetation has great capacity to loosen and lever off even very large lumps of rock. Once sound placements have been known to change as the rock around them unexpectedly crumbles.
Depth & Position of Bolt
Bolts placed close to edges will have a reduced strength; 200mm is often quoted as a minimum clearance distance. Unfortunately bulging limestone doesn’t usually accommodate bolts being placed with that allowable distance. Likewise, bolts placed close to cracks, pockets or other discontinuities may well be reduced in strength.
Evidence of Corrosion (Rust)
....Just because a bolt is rusty it doesn’t mean it is dramatically weakened. However, if it is rusty it has lost some metal and consequently some of its holding capacity. It is not unknown for the nut to be of a different metal and to have corroded so that it no longer holds the hanger in place. Bolts where the hanger is fresh and shiny but the bolt itself is rusty may suffer from a particular form of corrosion and have been known to break with the lightest of load. It makes sense to inspect bolts that are placed in drainage lines. Unfortunately the wettest place part of a bolt is in the hole and behind the hanger making inspection difficult.
Accidental Unclipping
Hangers or eyes ideally should be of a size that they don’t allow the karabiner to snag in such a way that the gate can be forced open and unclip. Correct orientation of the karabiner gate away from the direction of travel also helps avoid this.
Spinning Hangers
Hangers can spin because the bolt has moved in its seating or because the securing nut has become loose. If there is evidence of the former then the bolt is likely to be unsafe. If the latter is the cause then the nut should be immediately retightened. The leverage and wear caused by a weighted hanger rotating on the bolt body can give rise to weakening of the unit due to the formation of microscopic fractures.
Old Bolts
Despite the number of renewal programmes there are still many old bolts out there, especially ones used to protect blank sections on 80’s trad routes. Common sense dictates that bolts have a limited useful life and it is always worth consulting the guidebook to see when the route was first done or, if the gear has been replaced, when that might have been done. Whilst stainless steel products are likely to be good for a lot longer, experience has shown that many bolts placed in the past are dangerously weak after 10 years. Some early staples had no notches on their legs making them prone to pulling out relatively easily if an outwards force is applied.
Wobbly or Damaged Bolts - Mechanical or Glue-Ins
It makes sense to doubt the holding power of any bolt that wobbles in its hole! With glue-in bolts a problem can arise if the drill dust is not thoroughly cleaned out of the hole or if it was placed in a damp hole. Some wobbly glue-ins have been found to take quite high loads but it’s probably not sensible to test these with your own weight!
Unset Glue
Glues have to be mixed properly. Failure to do as instructed can result in the mixture not curing, or hardening as was designed and not holding the bolt in place. Several serious accidents have happened when climbers have come across new bolts and attempted the route without checking the glue has set.
Deteriorating Glue
Like the bolts themselves the glue can and will deteriorate with time though for appropriate glues this should be a very slow process. However, there is anecdotal evidence that some inappropriate glues have been used, that are not suitable for the alkaline solutions likely to be encountered in limestone rocks. Unfortunately this could mean that once sound bolts become less so, perhaps as little as two years after placement.
Worn Belay Bolts
If top-roping a route the climber can always arrange slings so that both bolts are weighted. This is good practice and climbers should be discouraged from top roping with the rope directly through the belay bolts, as significant wear on the eye can quickly result.
Home Made Hangers
Various types of bolt hanger were homemade during the 1950s and 60s. Usually these were simple angle iron (or aluminium alloy) with holes drilled in each side. A few may still be encountered on old aid routes today but generally they are now of little relevance and most have been superseded by modern bolts or other forms of protection
Stress Corrosion cracking
Although there is no evidence of this type of attack occurring in the UK, a number of bolts have failed by stress corrosion cracking (SCC) in Thailand and Cayman Brac so it’s worth being aware of it if you’re going sport climbing in the tropics. SCC can occur in stainless steels in aqueous chloride solutions (e.g., seawater) so the bolts on sea cliffs appear to be most susceptible. Luckily for us, there is a temperature (~50°C) below which it doesn’t occur (except in very acidic conditions) so it shouldn’t be a problem in the UK until global warming really kicks in. The corrosion is very localised and takes the form of cracks that can penetrate through the metal, reducing its strength to almost zero. These cracks can be very fine and difficult to detect on the surface and impossible to see how far they penetrate
There is also a part II. This goes into details on how to go about actually replacing the bolts.
When it comes to removing the bolts, it depends....You can sometimes unscrew them, sometimes the need chopping. TBH, it doesn't matter as you should drill a new hole, etc. for any new bolts anyway. Just make it obvious that the old bolts should not be used/remove them as best you can.
I'm guessing from how you phrased your question that you are really interested in how rebolting, specifically bolt removal, is performed. I have never rebolted anything, but the ASCA (American Safe Climbing Association) has pretty thorough articles for people interested in learning how to rebolt climbs here.
It goes over the following topics in very good detail:
