Mana as such is in a constant state of circulation. However, it requires a trigger, which is where the existence of incantations or chants come into play. This was knowledge Nate gained from his experience in Genesis.
If a part of the crystal were to be cut, it would have to be done with extreme precision, it would require someone who could feel and understand its application, someone exactly like Nate. A single mistake and the entire crystal would lose its strength.
Assuming the part was successfully cut off, the next step would be to capture its utility, and to do that, a material that could adapt and allow for such energy to flow through it must be used. There were a few options that they could easily get their hands on but the best option is something only blacksmiths would truly know.