As stated above, the cable end should slip right out with little to no effort. Some penetrating oil will not hurt, but try to keep it contained to the cable end, and not get it on any other parts of the speedometer; especially the numbering. Using a pliers as 1930 coupe suggested maybe all that's needed.
How does the speedometer turn? Grab the broken cable end and twist it with you fingers; it should turn with very little effort. (Something had to cause that cable to twist in two.)
Mine quit turning a couple of years ago, and the grease in the speedometer became hard and really made it turn very hard. I spent a lot of time getting that old grease out and re-lubricating it. But once I did that it turned smooth as silk. Good luck.