Back in 1970's I damaged a quality bit in my impatience to remove it when stuck. I first thied a piece of pine but it wouldn't budge so i used a screwdriver and the carbide was chipped due to my haste. There was no apparent damage within the collet to cause it to jam.
I came up with this VERY SIMPLE solution when it happened again. I always keep several wedges on hand at all times for various purposes esp clamping (2 working in opposite directions and tapped together).
The large wedges are great to raise heavy machines when fitting the fourth side to a mobile stand as I dont own a purpose made lifter. Use a mallet or dead blow first before resorting to brute force with a lump hammer or bigger.
This one is made from 3" treated H4 pine at about 8 degrees, but any softish timber with a little "give" would suffice. I simply routed slots in a couple of these for 1/4" shanks & 1/2 " shank bits: I dont have many 8mm ones. Raise the bit until you get some of the wedge under the perimeter of the bit and tap it into the shank and the v forces the bit out of the collet.
Recently (when this pic was taken) I was cutting grooves through a template which required an extension collet which became stuck. The wedge tool eased it out easily also.