No, you do not need a garbage disposal to have a dishwasher. A dishwasher will work without one, and while it's rare to see a home with a dishwasher that doesn't have a disposal, it is possible. The two appliances pair well and are often installed together because a disposal simplifies meal cleanup.

However, your dishwasher should not be used as a replacement for a garbage disposal. Subjecting it to continuous food leftovers can lead to major clogs. If you choose not to install a garbage disposal, you should thoroughly rinse your plates or scrape excess food into the trash or a compost pile before loading them into the dishwasher to prevent plumbing issues.

The two main negatives of garbage disposals are they are a safety hazard in homes with children, and they frequently encounter blockage issues. While they might be annoying to fix and monitor, garbage disposals can significantly lower your trash use and are a great way to dispose of organic waste. While there are negatives, the vast majority of homeowners acknowledge the positives are enough to install a disposal in their home. 

The most common garbage disposal size in the U.S. is 1/2 horsepower. This size is ideal for households with three or fewer people or those that don't produce much food waste. Although 1/2 horsepower can't handle the typical food waste load for a household of four (which is about 250 pounds of food waste annually) as effectively as 3/4 horsepower, it remains the most common size of garbage disposal on the market.

Once you have your garbage disposal disconnected, you can remove the mounting bracket by unscrewing the bolts that are holding the bracket. You can back them out just enough to pop off the snap ring, which prevents the bottom portion of the bracket from disconnecting from the top when you unscrew the bolts. Use a regular screwdriver to pop off the snap ring, and the rest of the components should fall off by themselves.