People have done cut boards in various orientations before but as Ben noted there are 6 layers in there that will potentially end up randomly touching. There is also the fact that dremeling fiberglass is really not a good idea unless you have some serious dust control. And a way to get that fibre+copper dustout of the Teensy once you are done (seal the keep end of the PCB?)
I'd differ from Ben though in saying that it could be done if:
You are prepared to blow several boards learning how to do it (this could be expensive)
You have some method to test all the needed parts of the board once you are done (breadboard/pogopins) before soldering for vibration damage during the cut
You come up with some way to test the critical connections with a meter as still seperate (gnd/3.3V/5V) against an uncut board
You make sure your code never activates the pins in the cut end of the board (including the now removed SD card)
You can accept slightly higher power consumption
You can accept a couple of pins not working post this process - It would be unusual if the PCB routeing took any signals out into the cut area and then back to pins in the keep area, but only way to find out is to do it*
You are happy to accept advice from people on the internet who may be trolling you into something expensive
*someone making a narrow Teensy 3.2 by shaving the outsides off took out pin connections that looped outside the holes and into the cut area
This is based on the fact that teensy pins are disabled on power up, so you can have pin to pin, pin to 3.3V and pin to gnd connection without trouble as long as you never once enable the pins, only cost will be slightly leakage current through those pins if they are in contact with 3.3V. What you cannot have is 5V connected to anything, hence advice to check the resistance values post cut before powering up. If you do find a connection it will be a case of some tedious work with a magnfier and a knife. Though if you have PCB etchant it might also be possible to hang the cut end in it to strip back all the exposed copper from the cutting (hopefully without dissolving anything you need).
Overall you need to consider the first and last points above against how much you need a sawn off board, and how much you are prepared to pay to learn if it is possible.