I was going to cut my 128k mini-sim down to size but then noticed Vodafone Italy had a free nano-sim available as replacement. I did practice on an old mini-sim and it was easy to cut to size with sharp electrician's scissors, then the only filing with sand-paper that I did was to smoothen the rough edges on the sim. The depth of the cut-down sim wasn't a particular problem.
practice on something old first!