Place tenderloins in a large shallow container. Combine pineapple juice, ginger root, soy sauce, garlic and mustard. Stir well. Pour over the tenderloins. Cover and refrigerate at least 8 hours, turning the tenderloins occasionally.
Remove the tenderloins from the marinade. Insert a meat thermometer into one tenderloin, making sure it does not touch any fat.
Grill over medium coals for 50 to 55 minutes, or until the thermometer registers 160 degrees. Turn the tenderloins occasionally. Let stand 10 to 15 minutes once they are done before slicing.
Grill the pineapple slices over medium coals for 1 minute on each side.
Slice the tenderloin, and serve with the pineapple slices.