(And if We let man taste mercy from Us)
That is, if We bestow upon him a blessing of health, security, prosperity, and the like, and convey it to him in such a way that he perceives its delight; thus, "tasting" is a metaphor for this bestowal.
(Then We remove it from him)
That is, We strip that mercy away from him. This is linked to the removal, and the use of this specific expression is to signify the intensity of his attachment to it and his greed for it.
(Indeed, he is despairing)
He is profoundly and excessively despairing, cutting off his hope for the return of such a blessing, whether sooner or later, through the grace of God Almighty, due to his lack of patience, lack of reliance upon Him, Exalted is He, and lack of trust in Him.
(Ungrateful)
He is one who excessively denies the previous blessings that God Almighty has bestowed upon him. This description is delayed after the description of his despair to preserve the rhythmic endings of the verses, although despair is also a form of denying the previous blessing.