Combine water, salt, and 1 tablespoon vinegar in a large glass mixing bowl; stir well.
Peel and slice each mango, and immediately drop into acidulated water. Rinse and drain in cold water.
Grind together mango, onion, and garlic in a stainless steel stockpot, using coarse blade of meat grinder. Stir in remaining ingredients, mixing well. Cover and let stand at room temperature overnight.
Cook over medium heat, stirring frequently, until mixture thickens.
Quickly ladle chutney into hot sterilized jars, leaving 1/2-inch head space. Remove air bubbles. Cover at once with metal lids, and screw bands tight. Process in boiling-water bath 15 minutes.