Do all Naturopathic doctors utilize spirituality and mystical practices?
The short answer is: "No"; each ND is different and unique.
Even among those who do utilize "mystical" and "spiritual" practices, a more thorough response to the question really hinges on two qualifiers:
1) what is meant by "mystical" and "spiritual"
2) which Naturopathic doctor one encounters.
"Mystical" and "Spiritual" are broad terms that may be understood differently. So it may be difficult to give a specific generalized response. Many Naturopathic doctors believe in the spiritual dimension of the human person and that this dimension is important for health. However, each Naturopathic doctor will apply and understand this differently.
Also, typically when this question is asked, the questioner is often referring to practices like: yoga, trancendental meditation, belief in chakras, or even things like healing crystals and stones. If these practices are what is meant by the question, then again, the answer is "NO." Not all Naturopathic doctors believe in nor utilize these practices. But some do.
If a Naturopathic Doctor states that they utilize "spirituality," are "spiritual" or something along those lines, do not jump to the conclusion that these automatically mean the practices stated above: healing crystals, chakras, etc. Ask the Naturopathic doctor about these things. It is your right as a patient to know these things about your clinician.
In conclusion: Some Naturopathic doctors emphasize the spiritual, some are into mysticism. Some integrate these things heavily into their practice while others less so, and many even ignore it altogether. Even among those who utilize it, definitions may vary. Thus, it would be erroneous to generalize one way or the other. If this is of interest to you, it is best to have an open talk with your present or potential Naturopathic doctor.