How to cut a mug without breaking it? This question is a kind follow up to this other question.
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:

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:
  

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?
A grit edged hacksaw blade (random example) would be the hand tool for the job.  It would be a bit of a slow job but not unreasonable (given the rate these things go through tiles).  

I suggest making/modifying a jig based on a mitre box to go with it, if you want repeatable, straight cuts. The jig itself might be a bit tricky as it sounds like you want straight, repeatable cuts. You should be able to cast modelling clay, plaster (or even hot glue) around a mug to around half depth using cooking oil as a mould release, all inside a home made or cheap mitre box. Then clamping the workpiece down would be a good idea. 

Like with power tools, work wet.  Unlike power tools you need frequent (rather than continuous) water delivery -- though the latter would do no harm.