How to cut a mug without breaking it?
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.