Peel the cucumbers and cut into chunks. Puree in batches in a food processor. Press the cucumber puree through a fine mesh sieve set over a bowl to catch the juices. Measure 1 1/2 cups cucumber juice.
In a 6- to 8-qt. stainless-steel, enamel, or nonstick heavy pot combine the cucumber juice, sugar, and vinegar. Bring to boiling over high heat, stirring to dissolve sugar. Quickly stir in pectin and mint. Bring to a full rolling boil, stirring constantly. Boil hard 1 minute, stirring constantly. Remove from heat. Quickly skim off any foam with a metal spoon. Using a slotted spoon, remove and discard mint. Stir in food coloring.
Ladle hot jelly into hot sterilized half-pint canning jars, leaving a 1/4-inch headspace. Wipe jar rims; adjust lids and screw bands.
Process filled jars in a boiling-water canner 5 minutes (start timing when water returns to boiling). Remove jars from canner; cool on wire racks.