The part(s) or condition(s) listed below for the symptom Garbage disposer stopper switch won't shut off disposer are ordered from most likely to least likely to occur. Check or test each item, starting with the items at the top of the page.
The start switch might be shorted out. Use a multimeter to test the start switch for continuity. If the start switch has continuity all of the time, this indicates that the start switch is shorted out. If the start switch is shorted out, replace it.
If the disposer uses a wall switch to turn power on and off to an outlet under the sink, or directly to the disposer, the wall switch may be defective and will need to be replaced by a qualfied electrician. If the garbage disposer is plugged in, you can unplug it or turn off the circuit breaker until the wall switch is replaced.
If your disposer uses the stopper to turn the unit on and off, and it won't shut off, the start switch is either stuck or damaged. You can try removing and reinserting the stopper several times to attempt to get the start switch to work properly. If the unit still keeps running, the start switch will need to be replaced. To keep the disposer from running, you will have to either unplug the power cord or shut off the breaker to the garbage disposer.