Suggest you use the method used on petrol lawnmowers...tightening and slacking a vee belt. You have an induction motor which prefers to run at a constant speed. Mucking about with it will blow the capacitor that is mounted on the casing. As the mixer is turned via a vee belt you need to introduce a clutch mechanism using the vee belt. Get a slightly longer vee belt and a matching small pulley so you have the belt running over 3 pulleys. The 3rd pulley is on a swinging arm that can adjust the tension, thus the speed. For slow you just slip the belt, and fast tighten. This method is used on top loading washing machines. Some have a gearbox combined with the motor. Depends how handy you are. The Lightburn [1960] washing machine was actually made by a cement mixer manufacturer, so it has been done before.
