Please for the sake of the injured person YSK that this is an ABSOLUTE LAST RESORT in the event that literally nothing else will stop the bleeding.

Tourniquets tend to cause severe long term circulation and nerve damage and 90% of the time are not needed to control bleeding. Only the more advanced first aid courses teach you how to control bleeding by cutting off circulation to an artery and even then it is taught as a last resort after all else fails because of the risk of permanent damage. Even doing it properly (knowing exactly where to jam your fingers to block an artery) you run the risk of collapsing the artery permanently.

This is what you should do first:

Take a local first aid course so you actually know what to do when something like this happens. Usually a one day affair held on a weekend. Best investment you can make for the safety of your family.

Anyways:

First apply direct pressure to the injury and wait for five minutes then check to see if the bleeding has slowed or stopped. If it hasnt stopped apply direct pressure and wait an additional five minutes. If after that the bleeding hasn't stopped THEN you can attempt to stop the bleeding by cutting off the circulation.

Person loses a hand? Apply direct pressure to the wound.

Chopped off at the forarm? Direct pressure at wound.

Missing a big chunk out of a limb? Direct pressure first.

Seeing a theme here?

By applying pressure to the wound you will stop them from bleeding out.

Hopefully, you are in a situation where emergency services can be summoned and you can just stay there applying pressure until they arrive. If for some reason you can't get help, and the bleeding won't stop, then it's time to think about using a tourniquet, or in an extremely unfortunate or unlikely scenario, using OP's method.