One of the nastiest maintenance jobs on standard automobiles. This work is easy to hand off to a muffler shop (not fun places to work by the way), which often provide (single) owner lifetime warranty as part of the job.
The difficulty of repairing exhaust parts is due to the combination of high temperature and environmental exposure of the pipes, fittings and mufflers, which causes more corrosion than in other parts of the vehicle. Unless the vehicle happens to be one of the rare examples to use stainless steel muffler parts, as little as a year in service will render the fasteners difficult to take apart without breaking them.
The reason that most people farm out this work rather than tackling it at home (beyond the inherent discomfort of working on parts which like to drop little showers of rust particles into the mechanic's eyes) is the lack of the essential tool - the oxy-acetylene cutting torch.
If you happen to have an available cutting torch, the most difficult work becomes far easier, one can simply cut off the parts (a reciprocating saw is a very good second choice). Warning -- the underside of an auto may include grease, oils, plastic and anti-rust coatings and GASOLINE - both in fuel lines and the fuel tank. All of these things are flammable, and possibly explosive in the presence of the pure oxygen used in the cutting torch.
While this is the standard method used in shops to remove exhaust parts, the mechanic needs to plan very carefully where and how the torch will be used. Cutting a fuel line or tank with a torch (or an electric saw) would very likely prove fatal. Think carefully about where the torch is pointing as you work.
In the event that one chooses to disassemble an exhaust system using hand tools, the following observations should help to guide the work.(And if you put it together last time using anti-seize compound some of what follows may thankfully not be true.)
- Studs and bolts which mount to the exhaust manifold(s) or engine must be handled carefully, stripping a thread here is costly
- other threads often cannot be disassembled, use a hacksaw or nut breaker
- Where pipes are joined by a clamp they will rust together quite solidly
- Techniques to free rust frozen parts
- early application of solvents (brand name liquid wrench) is helpful
- Application of heat - usually propane or mapp gas torch - thermal expansion can help to free parts (warnings above apply)
- Careful application of force, a hammer can be used to help free parts
- Hammer blows (still careful ones) can also help drive liquid wrench into crevices
- All of the above are useful in iteration, using all of the above will be faster than using any one.
- Wear goggles, rust particles in the eyes are not fun.
With patience and care it is usually possible to remove the defunct parts and not destroy the ones that are still usable.
As you work, let the difficulties remind you that when you install the new parts, application of anti seize compound to every part that was difficult will simplify disassembly next time. In this experience is an excellent teacher. Generally, taking care of problems in the exhaust system early will save trouble in the long run.