To analyze this question, we first need to clearly identify the themes and understand the meaning of the word used in the title.
The themes of this poem include the mother-daughter relationship and the changes that happen when children become more independent. In this case, that independence is exemplified by the daughter getting a haircut without the mother's permission or influence. The words used to talk about the haircut include "knife grinder," "sharpened," "paper-cuts," "carbon steel," and "blade." The poet alludes to the daughter being of her body, and so the references to knives and cutting can be seen as a representation of both the severing of the umbilical cord and to the idiom to "cut the apron strings." The poem then changes to using the imagery of war: resin helmet, watch fires, enemy, and in the final line, there is reference to an impending war. This imagery indicates that the relationship is going to change to an adversarial one. From the softness in the first stanza when the poet talks about her daughter's "wispy hair like a bellpull" to the penultimate stanza's "great distance," we can see this change.
So, having identified the themes we can move on to the title and how it relates to those themes. The word possessive can be interpreted a number of different ways. The first way is using synonyms like controlling, jealous, protective, and obsessive. We can talk about a relationship being possessive when one person has control over the other or when one person tries to have control over another. This links into the other meaning of the word, related to the term "possessed." We can think of possessed as meaning to be haunted, or entranced, by a mischievous or evil spirit.
The poet plays on the first meaning of the word by painting herself as a possessive mother; in the first line she refers to her daughter "as if I owned her." She also refers to the daughter's hair being "wispy as a frayed bellpull." Here, the mother is alluding to the control that she previously had over her daughter, much like a person controls a bellpull. Throughout the poem, the mother can feel her control over the daughter slipping away, and the poem ends with references to the increasing distance between them.
The poet plays on the second meaning of the word with references to her daughter's eyes: the daughter has "distant fires" in the "resin light" of her eyes. This imagery of the daughter's eyes burning is an allusion to the red eyes that people get when they are said to be possessed. The mother also feels that her daughter is a different person; she says she will "have to find another word" to describe her (other than "daughter").
Another less obvious reference the word "possessive" makes is to the word "self-possessed." This means to be stubborn or confident. This meaning can also refer to the theme of the changing mother-daughter relationship and the ways in which the daughter's character is changing from obedient and docile to headstrong and independent.