Combine beef and barbecue sauce in slow cooker. Cook on low for 6 to 10 hours or on high for 6 hours. When done, shred the meat by pulling against the grain of the meat with two forks.
To assemble the quesadillas: On one half of each tortilla, spread 1/2 cup beef, 1/4 of the mango, 1/4 of the red onion, and 1/4 cup cheese. Fold the empty half over the filled half and either place on a lightly oiled grill or frying pan for 2-3 minutes per side, until the cheese melts.
*Note: This recipe makes more beef than you will use in the quesadillas.