Preheat a grill to medium high and brush the grates with olive oil. Pierce the sweet potatoes all over with a fork and microwave until just cooked through, 5 to 7 minutes; let cool slightly, then slice into 1/2-inch-thick rounds. Transfer the sweet potatoes to a medium bowl and gently toss with 1 tablespoon olive oil, 1/4 teaspoon salt and a few grinds of pepper.
Meanwhile, toss the cucumbers, pineapple, scallion, cilantro and vinegar in a medium bowl; season with salt and pepper. Set aside. Mix the brown sugar, chile powder, cumin, 3/4 teaspoon salt and a few grinds of pepper in a separate bowl. Rub the pork all over with the remaining 1 tablespoon olive oil and the spice mixture.
Grill the pork, covered, turning occasionally, until a thermometer inserted into the center registers 145 degrees F, about 15 minutes. Remove to a cutting board and let rest 5 minutes. Grill the sweet potatoes, turning once, until marked, about 3 minutes. Slice the pork and top with the cucumber-pineapple salsa. Serve with the sweet potatoes.