Assuming this is a classic Mini, there are several possibilities.  The following two are the first that come to my mind.

1) If the car has a ballast ignition system, the white/pink wire from the ignition switch could have failed... or the ignition switch may have failed.  While cranking, the coil would be getting power from the white/yellow wire on coil (+).  When you release the key... there is no power supplied to the coil so the engine dies.
2) If the car has a standard ignition system, you could simply have a fault with the ignition switch.

Carefully look at the wires on the ignition coil and post a reply noting what color wires are connected where.

It would be helpful to know if it's a real Mini, or a BMW...

I’m having trouble starting my mini. I have power all over the car. When I go to start it starts but as soon as I let go of the key from the staring position it shuts off. Idk what to do.