What type of poem is "On Killing a Tree"?

"On Killing a Tree" is a poem by the Indian poet Gieve Patel. It is a protest poem, written in stanzas of irregular length. It does not use the traditional markers of poetry, such as rhyme, regular meter, or stanzas of equal length. Instead, it is written in what we call free verse.
Free verse can often be difficult to differentiate from prose, in that it has no strict meter or rhythm. Unlike blank verse, which tends to use an iambic pentameter despite the fact that it does not rhyme, free verse follows the rhythms only of conversation. However, this poem is laid out in a way that makes it obviously poetry rather than prose; the irregularity of it allows the poet to make statements with his choices as to where new lines begin and end. Isolating "No," for example, makes the word seem definitive, as if the poet has come to and is reiterating his decision about killing a tree being a difficult and deliberate action.
Free verse poetry often utilizes alternative techniques in order to lend internal cohesion to the poem. In this poem, we see parallelism ("pulled out—snapped out—/ Or pulled out entirely") and assonance (note the repeated use of "ing," which emphasizes also the active nature of what is being done to the tree).