(1) Background: Dog-assisted therapy (DAT) is an experiential intervention to promote psychological, physical, and social functioning in children and adults. Only few studies have been conducted on DAT in adults with a mild intellectual disability or borderline intellectual functioning (MID-BIF). The purpose of this study was to explore the experiences of patients with MID-BIF undergoing DAT in a mental health care facility. (2) Method: Seven patients completed 13 to 15 sessions of DAT. Within two weeks of completing the program, they were interviewed using a semi-structured interview. The transcripts of the interviews were analysed using interpretational phenomenological analysis. In addition, the patients’ relatives and the DAT therapist were interviewed, and a focus group discussion took place with each patient’s treatment team. (3) Results: The patients’ experiences were predominantly positive. Physical contact with the dog calmed them down. The dog offered them emotional support and helped them to make contact inside and outside the therapy and the setting where they lived. The patients also liked the fact that DAT focused on the dog rather than their problems, that the therapy was experiential and using a positive approach, and that, during the therapy, they did not feel like a patient but a human being. DAT is a promising therapy for patients with MID-BIF in mental health care facilities, but more research into its effectiveness and cost-effectiveness and ways to implement DAT in clinical practice is needed to make more definitive statements.