Big branding changes hit the model lineup for the Mark III iteration in 1970 because the vehicle was simply called the Mini with no longer any reference to Austin or Morris.
In terms of design, the exposed door hinges were gone, and all models now had roll-up windows. The rear side windows were a little bigger, too.
The Cooper and Cooper S also bowed out during this generation. However, the 1275GT kept the torch burning for performance-loving Mini fans.