I would do this quite differently .

Frame 1 , Face at rest

Frame 40 Face at rest
Frame 60 Face smiling
Frame 80 Face at rest

With keyframes as shown , the anim would run for just under 3 seconds
the fiure will take 2/3 of a second to go from rest position to full smile , and another 2/3 second to go back to rest .

Adjusting the frame 40 and 80 keyframe position to control how fast the change occurs.

These extra keyframes help you shape the spline interpolation of the movements .

Break spline is also useful for abrupt changes in direction, or for  odd effects .

A term often used in animation is "ease-in"  or ease-out.   Any books on Keyframe animation will have suggestions on  setting up smooth actions.

Mimic should create an animated pose with only the mouth movements. I would apply the mimic pose first, then add any changes to the characters face.

Or you can learn to edit the mimic pose file and remove the unwanted morph settings .