The previous educator answer has identified the primary type of metaphor used in this poem: personification. While, of course, not all metaphor is personification, personification is a particular type of metaphor in which an inanimate object is described as if it were human, and ascribed human characteristics and motivations. In this poem, the saw is personified throughout: the speaker imagines it behaving as if it "knew what supper meant," reacting to the words of the boy's sister.

Another example of metaphor derives from this prevailing type, then, when we see the connection between the saw and the boy's hand described as a "meeting." This is an interesting choice of words: it suggests that there is, in the moment, nothing violent about the connection; it is seemingly voluntary. This helps us to understand how it looked to an observer, the strange inevitability of the hand, tragically, encountering the saw without resistance.

Afterwards, the boy holds up his hand as if to "keep the life from spilling." Here, "blood" is implied, but the word "life" is used to represent it, as if the boy could prevent his life from pouring out of his wounded hand in the form of blood.

Finally, the boy descends into the "dark of ether," not a literal darkness, but a metaphorical twilight world which precedes the darkness of death itself.

Personification is a distinctly different type of figurative language than metaphor. Metaphors are implied comparisons between unlike things to illustrate a point. On the other hand, personification ascribes human qualities to a non-human thing.

In “Out, Out—“ by Robert Frost, personification is the primary figurative language used throughout the poem with the saw. However, Frost does use metaphor, albeit sparingly.

When the speaker describes the saw cutting into the boy’s hand, he says the hand tries to “keep the life from spilling.” This is an example of metaphor because blood is being referred to as life itself. This foreshadows the ending of the poem.

After the doctor amputated the boy’s hand, the doctor “put him in the dark of ether.” This is a metaphor because it compares a state of unconsciousness to the dark. This metaphor continues the foreshadowing of the first about life spilling. Once the boy goes into the darkness, he does not return.

Metaphor is a comparison of two different things.  When you compare something to a human, that is a type of metaphor called personification.  Poets use metaphor to evoke a mental image.  In this moving poem about a farmer losing a hand, it is the stark language and disturbing images that add to the reader’s reaction.

The buzz saw is described as having “snarled and rattled” (line 1).  A saw can rattle, but it can’t actually snarl.

The saw is then described in the same way a human would be.

At the word, the saw,

As if it meant to prove saws know what supper meant,

Leaped out at the boy's hand, or seemed to leap -

He must have given the hand. (14-16)

The saw cannot leap, and the saw is personified as thinking about supper.  The poem ends as the boy dies.

And they, since they

Were not the one dead, turned to their affairs. (29-30)

The contrast between the imagery and the harsh reality is quite effective and disturbing.

Are there examples of imagery, allusion, or hyperbole in the poem 'Out, Out--' by Robert Frost?

This poem, which is based on a real-life event, is full of striking images. The most impressive one, in my opinion, occurs early in the poem when the narrator describes "five mountain ranges one behind the other under the sunset far into Vermont." Try to visualize five pointed mountains; it's not hard to imagine that Frost is foreshadowing the teeth of the buzz-saw. That he uses the number five, furthermore, and notes that the time of day is sunset suggests the boy's bloody hand with five fingers.

The title of the poem is allusion to Shakespeare's play Macbeth. In a soliloquy late in the play, Macbeth compares life to a candle: "Out, out brief candle!" he says, noting the brevity and frailty of life as Frost's poem also does.

For hyperbole, I think perhaps the repetition of the buzz saw's noise ("snarled and rattled"---onomatopoeia) may be exaggeration to call the reader's attention to the danger of the tool. From a different perspective, the callousness of the boy's parents may also be exaggerated by their apparent absence until the end of the poem. Where are they when the boy and his sister are working? Why is this "big boy doing a man's work though a child at heart"? Notice that the boy calls to his sister for help, not his parents. At the end of the poem when the boy dies, "they" may refer to his parents; if so, "they, since they were not the one dead, turned to their affairs" suggests an indifference that may also be an exaggeration.