Depends what you mean by "mystical." There are two general usages of the word, one roughly corresponding with supernatural and the other with spiritual.
Considering that D&D includes all kind of supernatural phenomena, and thus--in the context of D&D--the supernatural is more "hypernatural," meaning an extension of nature rather than something outside or opposed to natural law--a lot could be considered mystical in that way, to the point that it wouldn't really make sense except to consider the degree to which a race engages with magic and related phenomena. In the D&D world(s), many/most races relate with magic to some degree or other, although some (elves) more than others (halflings).
Mystical as in spiritual presents a more complex and subtle discussion, with mysticism being a wide range of practices that involve an individual relating to domains of experience that most consider superstition and/or hallucinatory. Yet there is a whole field of psychology that deals with this question: transpersonal psychology, and related fields such as Jungian, archetypal, and others.
Various more recent formulations have posited that there are different, broad domains of being: the physical, which is everything that we can interact with via our senses; the vital, which has to to do with subtle energy or life-force (e.g. the prana of yoga or chi/qi of traditional chinese practices); the mental, which is the psychological domain of thought and feeling; and then what we could call the mystical, which is everything beyond the physical-vital-mental matrix that we are all aware of, to different degrees (we sense and interact with the physical world; we are alive; and we think and have feelings, but most of us are not cognizant of mystical realities). We could also add a higher domain, the spiritual, which is divine Oneness.
Mystical practices include, but are not limited to, meditation, trance, shamanic practices (e.g. journeying), psychedelics, breath-work, active imagination, sensory depravation, and so on. Different practices and traditions have different goals; some seek to engage with the "mystical" domain, perhaps for deeper knowledge or insight; some might work on the vital level for healing; some are about calming the mental chatter. Some feel that "true" mysticism is about recognizing the realm of pure spirit, or oneness, and thus everything else is to be bypassed on the way "up."
So with all that in mind, to approach the idea of a "mystical race," we need to have a sense of what that means. Is it a race that recognizes the mystical and/or spiritual domains? Or merely one for whom the supernatural (or hypernatural, aka magical) is a living reality? Again, if the latter, well, that's many or even most races and creatures in D&D to varying degrees, so the question is really a matter of "to what degree."
But if the former, then I think you're talking about a race for whom the waking world is somewhat dream-like, an appearance that "masks" a truer reality - one in which mystical entities exist, and that the underlying nature of reality is a kind of oneness of being that merely appears as the physical world. This could be treated in different ways, depending upon what you're after. Some might be dissociative, treating what we call reality as a dream; others might be more engaged, seeing it as the playing field for the machinations of gods, and with some kind of metaphysical goal in mind (for instance, the journey of souls back to oneness). Etc, etc.
