Make slaw. Mix together the mayonnaise, cider vinegar, Cajun seasoning, salt, sugar, pepper, and hot sauce together. Toss your carrots and cabbage in the mix and refrigerate for an hour before serving.
Remove external fat from the pork tenderloin. Season the pork tenderloin all over with Cajun seasoning. Set it aside at room temperature and preheat your grill to 350°F to 400°F.
Grill your tenderloin directly over the coals, rotating the meat every 5-6 minutes, until the pork tenderloin reaches an internal temperature of 145°F. This should take about 25 to 30 minutes.
Pull the meat off of the grill and let rest for at least 3 minutes. While the pork is resting, toast your slider buns over the hot coals.
Rub the minced garlic on a cutting board and then drizzle the BBQ sauce over it. Place the tenderloin on top of this and slice thinly, allowing the slices to fall over into the sauce. Build sandwiches and serve with slaw.