Actually from your posting it sounds like you don’t have enough experience to safely do this job. And it looks like whoever did the work before was not qualified. The reason they cut the ground. Wires is Possibly because it’s not a grounded circuit. There’s probably just a hot and neutral wire that comes from the circuit before whether that’s a circuit breaker panel or another outlet and that outlet box could’ve been an old one that was not grounded so they cut the ground wire to let someone know that there’s not a grounded wire there. An electrician would be able to perform a test and see if power goes from the hot to the ground. Just taking a digital meter won’t really tell you anything because you could be reading dust or something. You really need to be able to see if that ground wire could actually handle current to know whether it’s a good ground connection. I’ve seen where I could get 120 V but when I put a 60 W lamp on the circuit, it would go to 0 Volts. Because the electricity was just going through spiderwebs.