The Speaker
The poem's unnamed and unidentified speaker spends the poem urging their listener not to let loss affect or unnerve them. This speaker seems to hold a strong belief that it is unhelpful to react to loss with excessive emotion, and indeed, repeatedly states that people should lose things regularly so as to keep the feeling of loss in perspective. However, the speaker's manner of expressing themself shows that their true feelings differ from their stated stance. Their list of losses steadily builds up from the extremely minor to the very major, showing that they are unsuccessfully trying to deny feelings of grief by equating it with much less serious forms of loss. Moreover, the parenthetical phrase "Write it!" reveals the speaker's difficulty actually conveying the beliefs in the poem, and implies that they are much more affected by loss than they are willing to admit.
The mother
The speaker references the mother only briefly, when explaining that they have lost, among other items, their mother's watch. It is not entirely clear whether this watch is an inherited object handed down from a dead parent, or whether the speaker his simply lost an object belonging to their still-living mother. In either case, though, the loss of the watch implies a broader loss in the speaker's relationship with their mother: a death, an estrangement, or a conflict.
The "you"
In the final lines of "One Art," the speaker addresses an unknown character, referred to only via second-person pronouns. They evidently feel great tenderness for this person, and list things they miss about them—their voice and their gestures. The "you" is one of the many lost things listed in the poem, and is indeed the final loss listed, implying that it is the most serious and upsetting. Though the nature of the loss is not explicit, the speaker's expressions of grief and focus on the physicality of the lost loved one both indicate that the "you" has died.
