Working in batches, coarsely grind tomatoes, onions, red bell peppers, and green bell peppers in a grinder or food processor. Line a large colander with cheesecloth and place in the sink or a large bowl. Pour in tomato mixture to drain for 1 hour.
Combine drained tomato mixture, sugar, vinegar, celery seed, mustard seed, and salt in a large, non-aluminum stockpot over high heat; bring to a boil. Reduce heat to low and simmer, stirring frequently, for 5 minutes.
Sterilize enough jars and lids to hold relish (twelve 1-pint jars or six 1-quart jars). Pack relish into the sterilized jars, ensuring no spaces or air pockets. Fill the jars to the top; screw on the lids.
Place a rack in the bottom of a large stockpot and fill halfway with boiling water. Carefully lower the jars into the pot using a holder. Leave a 2-inch space between the jars. If necessary, pour in more boiling water until the tops of the jars are covered by 2 inches of water. Bring water to a full boil, then cover and process for 30 minutes.
Remove the jars from the pot and place them on a cloth-covered or wood surface, several inches apart, until cool. Once cool, press the top of each lid with a finger, ensuring that the seal is tight (the lid does not move up or down at all). Relish can be stored for up to a year.
