To test a telescope mirror in the shop, you need to hold the mirror so that the test jig can see it, so that it is adjustable in position and placement, and so that it does not inflict a change in the shape of the mirror due to stress from gravity or the test stand itself.
The mirror needs to be held so that it is pointing horizontally, therefore the edge of the mirror, not the back of the mirror, is supporting the weight of the mirror. There are two standard ways to do this so that the shape of the mirror is not altered. One way is with pegs, and the other way is with a strap. As for the pegs, they need to be mounted 90o from each other, one on the right and one on the left, which are actually 45o to the right and 45o to the left, a total of 90o of separation. The force of the one on the right may bend the mirror to the left, and the force on the left may bend the mirror to the right, and the concept is that they will counter each other and hopefully not cause an astigmatism in the glass.
The other way is to support the mirror with a strap. The strap needs to have 180o of contact on the glass, the right side will be forcing to the left and the left side will be forcing to the right, again countering each other. Also, if your strap is thin, or if you are using a cable, it ought to be at the center of gravity for the mirror. This is not exactly half-way from the front edge to the rear edge since the mirror is usually flat on the back and concave in the front. It would be slightly behind the halfway point.
One of the tests we do is an astigmatism test, and if it turns out that you see astigmatism in the optic, you would want to eliminate the test stand forces as the cause of the astigmatism. To do this you would rotate the mirror and see if the suspect astigmatism rotates with the mirror or stays in the same position. If it stays in the same position, your test stand needs changing [or your test method of astigmatism]. If it rotates with the mirror, then the mirror needs fixing. Also, if you are testing your mirror with a bath interferometer, it will see the astigmatism generated by the test stand. If you rotate the mirror into different positions and test with the interferometer, then the software will eliminate the warpage of the glass.
Your mirror test stand should have adjustments for tilt. Adjusting it for position is as easy as moving the test stand. Also your test jig will be able to go up and down. Your equipment should be built so that you donít have to go back and forth a jillion times between the mirror and the razor.