There is a spring.
One problem, apart from not cutting the SIM small enough, is that micro SIM cards are thicker than nanos and if there is any deformation from your cutting it will make it even more likely to get jammed. So as @urs_lesse has indicated try and remove it with something like a needle,
If you can’t get a needle into the surface try adding the smallest bit of supper glue to the needle, poke it in the edge, leave it to dry and try pulling it out and of course ensure that you DO NOT get any supper glue on the slot 
Maybe getting the needle in the edge at an angle will do, without glue.
Have fun ~ take care
The nano SIM is slimmer, thanks to thinner chips and more precise engineering, so the nano SIM is only .67mm thick.