This question is a kind follow up to [this other question][1].
Indeed, now that I know how to glue pieces of mugs, I'd like to know how to cut them. The idea is to get some cheap IKEA mugs with various colors such as this one:  
[![IKEA cup][6]](http://www.ikea.com/us/en/catalog/products/60143992/)  
Then I'd like to cut them into pieces (preferably not too many, say 3) so that I can reassemble them (by gluing the pieces). The goal is obviously to stick mug pieces of different colors together. For example, the cut should be along the red lines of one of the picture below:  
[![enter image description here][3]][3] [![enter image description here][4]][4] [![enter image description here][5]][5]

I'm open for other cutting lines if it makes the process easier. I'm also open to consider a different type of mugs but should say that minimizing the price is important as I potentially would like to make several of them.

My question: **Is cutting a mug as above possible and if yes, how?**


  [1]: http://crafts.stackexchange.com/questions/631/how-to-glue-mug-pieces
  [2]: https://i.sstatic.net/zxfjVm.jpg
  [3]: https://i.sstatic.net/9jwRcs.jpg
  [4]: https://i.sstatic.net/VhGwks.jpg
  [5]: https://i.sstatic.net/EJqCfs.jpg
  [6]: https://i.sstatic.net/v5SZb.png