Whisk together the vinegar, salt, garlic powder, basil, and red pepper flakes in a large glass or ceramic bowl. Add the pork chops and toss to coat. Cover the bowl with plastic wrap; marinate in the refrigerator 6 hours to overnight.
Preheat an outdoor grill for medium-high heat; lightly oil the grate.
While the grill heats, combine the cherries, water, and sugar in a saucepan over medium-low heat. Cook, stirring occasionally, until the sugar dissolves completely, 5 to 10 minutes.
Remove the pork chops from the marinade and shake off excess moisture. Discard the remaining marinade.
Cook the pork chops on the preheated grill until no longer pink in the center, 8 to 10 minutes per side. An instant-read thermometer inserted into the center should read 160 degrees F (70 degrees C).
Drizzle the chutney over the pork chops; garnish with the mint.