Slow draining of a garbage disposal can be caused by a number of problems.
- Assuming you've given the disposal enough time to run and clear the garbage, you probably have a clogged drain line.
- NOTE: Never use chemical drain cleaners with a garbage disposal! You will damage the disposal and since the chemicals probably won't work anyway, you'll end up with a sink full of toxic chemicals you'll have to hand bail into a bucket and flush down the toilet.
- Remove the bolts holding the discharge pipe to the disposal.
- Disconnect the drain trap and remove the trap and the discharge drain pipe.
- Check for clogs or obstructions.
- If none are found, the clog lies in the line going into the wall or beyond the vertical pipe going into the wall.
- Clear the obstruction with a sink auger.
See the Tutorial How to Unclog a Sink.