Do psychology deals with what others could call spiritualy? Does any branch of psychology study scientifically what traditionally, outside a scientific perspective has been called spiritually? In the same way people of ancient times considered voices in the head to be demons and we today consider that a mental issue related to schizophrenia.
Could the spirituality of other be the positive thinking, empathy, or any other aspect - empirically studied - of the mind?
Maybe what you are looking for is the field cognitive science of religion:

Cognitive science of religion is the study of religious thought and behavior from the perspective of the cognitive and evolutionary sciences. The field employs methods and theories from a very broad range of disciplines, including: cognitive psychology, evolutionary psychology, cognitive anthropology, artificial intelligence, neurotheology, developmental psychology, and archaeology. Scholars in this field seek to explain how human minds acquire, generate, and transmit religious thoughts, practices, and schemas by means of ordinary cognitive capacities.

Follow up resources:

International Association for the Cognitive Science of Religion (IACSR)
Journal for the Cognitive Science of Religion