Upper limb exoskeletons (ULEs) are robotic devices that can mobilize a severely disabled individual's arm and help the user perform some activities of daily living independently. Despite advancement in the mechanical design of ULEs, a versatile control interface that enables full and continuous control of a ULE with multiple degrees of freedom for a user with disability in both arms and legs (tetraplegia) still requires further research and development. In this study, ten individuals with tetraplegia used a tongue-based interface to fully control a five degrees of freedom ULE for a drinking and a snacking task. This required moving the ULE hand from a wheelchair armrest position to grasp an object (bottle or strawberry) placed on a table in front of the participant, moving the object towards them until it touched a face shield, and placing the object on the table. All participants successfully controlled the exoskeleton and completed the tasks. The drinking task lasted 149.6 s on the first day and 122.9 s (median) on the second day of using the exoskeleton. The participants performed the snacking task only on the first day of ULE use and achieved a median task time of 167.0 s. The study showed that the tongue interface could provide effective, efficient, and safe control of the exoskeleton.