Trim tough outer stalks from fennel. Cut bulb in half lengthwise; remove and discard core. Set bulb aside.
Cut tenderloin lengthwise down center, cutting to, but not through, bottom. Flip cut piece over to enlarge tenderloin, and sprinkle with salt and pepper.
Coat grill rack with cooking spray; place on grill over medium-hot coals (350° to 400°). Place tenderloin and fennel on rack; grill, covered, 5 minutes. Add mushrooms. Grill 5 additional minutes or until tenderloin is desired degree of doneness and vegetables are tender, turning tenderloin and vegetables once. Cut tenderloin and fennel into thin slices.
Arrange tenderloin, fennel, and mushrooms evenly over focaccia rounds. Spoon 2 tablespoons chutney over each round; top with cheese. Return to grill rack; grill 3 minutes or until cheese melts.