Zen "no-mind" (C., wu-shin/wuxin; J., mushin) doesn't mean to be without a mind or to be absent minded! The following might help us get oriented to this difficult term.
The term no-heart [no-mind] (wu-shin) comes from a Taoist background and was also used by the Buddhists. Chan [Zen] translates it as "no deliberate mind of one's own" or "no mind of one's own," and, in a Buddhist context, as "the non-being of the mind." As he explain in his discussion of the Neo-Taoism of Wang Pi (d. 249) and Kuo Hsiang (d. 312), the Taoist sage rises beyond all distinctions and contradictions while remaining in the midst of human affairs. "In dealing with things he has 'no deliberate mind of his own' (wu-shin) but responds to them spontaneously without any discrimination....The Buddhist Chi-tsang (d. 623) writes that it means "that one should not have an deliberate mind toward the myriad things" (Murata, Chittick, Jami, Wang, Chinese Gleams of Sufi Light, p. 54). (Brackets are mine.)
In the treatise On No-Mind attributed to Bodhidharma the term no-mind is never meant nor intended to leave us with the impression that no-mind is against direct intuition or awakening to something transcendent. A more pithy meaning for no-mind is "no discriminating mind." Such a no discriminating mind is the same as True Mind. In fact the treatise says: "Indeed, no-mind is nothing other than true mind. And true mind is nothing other than no-mind" (trans. App). Further on the treatise says: "What is called no-mind is nothing other than a mind free from deluded thought” (trans. App).
With that said, it is hard to escape from the spiritual duty to see our luminous Mind which is above and beyond the mind the deliberates and discriminates.