"You are children of Hashem your God; do not cut yourselves, nor make a baldness between your eyes for the dead. For you are a holy people to Hashem your God, and Hashem has chosen you to be a treasured people, from all peoples on earth. (14:1-2)
Let us start by noting that the phrase "between your eyes" must mean a location where there was originally hair, before being made bald. By comparison tefillin, which are also placed "between your eyes", must also be above the hairline. (see Menachot 36a)
The resemblance between tefillin and this prohibition may in fact be deeper. Excluding the Temple service, tefillin are the probably quintessential item of ritual holiness. Making a "baldness" on the tefillin spot, thus perhaps making it impossible to wear tefillin there, implies deliberately refusing this holiness. Thus, in way of explanation, the Torah explains that "you are a holy people" - a status which you may not refuse.
Furthermore, people who mutilate themselves (for suicidal or other reasons) apparently tend to cut their arms or wrists in particular. (This may be simply because the arm is the most accessible body part, and the wrist includes important blood vessels.) Thus, the "cutting yourself" referred to earlier in the verse may specifically refer to cutting the arm. If so, we have another connection to tefillin. The two examples of mutilation would refer to the arm and the forehead, the two places where tefillin are placed.
By comparison with tefillin, we can therefore explain both of the strange commandments in this passage, their juxtaposition with each other, as well as the explanation given for them.