There are several different ways you can cut copper pipes. All of them work effectively, but the method that is used is usually dependent on the tools available.
Using a Hacksaw
While it is the least recommended method of cutting, it is possible to cut a copper pipe with a hacksaw. Granted, it is one of the most common tools available, but when a copper pipe is cut with a hacksaw there is a lot of movement and a tendency for a untaught cut.
It is extremely difficult to be able to hold the pipe completely still while you cut. This is not a problem however if you are cutting a new piece of pipe for a system, as the pipe will be firmly locked in place.
It is important to note that if the pipe is already part of a system, be it a hot or cold water pipe, or a central heating pipe, It will move while being cut. This will put pressure on the nearest joint, potentially increasing the likelihood that the joint will fail.