While the color codes are really only specified for the house wiring and may not apply inside an appliance, usually the equipment ground is pretty obviously connected to some metal part of the appliance. Running off somewhere would seem perhaps to be another 120V function. Unless you can trace it and find it connected to the frame somewhere I'd not cut it.(and frankly, I've never had to cut a wire on either a dryer or range, the frame to grounded conductor connection is almost always under a screw somewhere). The GE Dryers I've have a strap from one of the terminal screws to the frame (within inches) of the terminals where the cord connects.

Trash that cord and buy another ... and DON'T TEST IT THAT WAY! Honestly, how do you expect plugging a bare cord into the outlet will "test" it when there's no device attached to it to receive the power and confirm the cord is working? The circuit breaker surely tripped. Seriously, maybe you should call a service tech or electrician to install the new cord. Appears you don't have experience with electricity, and some modification is needed on the dryer connection block to use a 3-wire cord vs. 4-wire.

Digital clock, right? Reusing it safely, without releasing its Magic Smoke, will require a little electronics background and some sleuthing. Because this was part of an appliance, you can't just buy a power cord for it and plug it in. You have to figure out for yourself where power is applied to the clock, and what that power is (240 volts, 120 volts, or maybe some other voltage provided by a transformer elsewhere in the range). If it was a gas range, it's almost surely 120 volts. If it was electric, it could be any of the above. My guess would be that the red and white wires supply 120 volts to the transformer (the large square black and white item). If I'm right, you'd connect those to your line cord - probably red to black and white to white. Connect the line cord's green wire to the metal box you make to enclose the clock to prevent shock.. (You ARE planning to do that, right?) But that's only a guess. If you want to use the clock to CONTROL something, not just check the time, that's going to be more of a challenge than just getting it to light up and count off the hours. If you don't have some electronics knowledge, the safe thing to do here is to recycle the old clock, and buy a premade one that does what you need.

Always watch a Youtube video when not sure how to do ANYTHING. The first thing you do is turn off power (from the electrical panel) or FULLY unplug any electrical appliance that you're going to work on. That wire is damaged...period. It may work but it's NOT SAFE. It can over heat and cause a devastating fire. I new cord isn't that expensive. And be VERY careful when installing it.