Damage when drilling a mirror — normal or not?
Is my cabinet maker correct


They are right that drilling clean holes in glass is more difficult than in wood or steel.

In my opinion, they are not right to say that visible cracking around the hole is normal. 

They are a professional and part of the price they charge is for having the skill, experience and tools to do the job better and quicker than you can. The hole on the right suggests they can get an acceptable result at least 50% of the time. In my opinion, they should have factored into their price the cost of wastage in redoing work where needed.


  should I ask for a new mirror?


That's up to you. If you are going to stare unhappily at that defect every time you use that cabinet then you should get it fixed now. 



How you do this is a matter of negotiation - because you probably don't have a written contract that specifies explicitly what constitutes an acceptable hole in the mirror.