In this poem, the speaker's tone is calm, even flat. There is a calmness to the speaker's tone that causes the reader to realize death is a natural part of life. 

The speaker is as a ghost or spirit. She is watching the events that take place at death. She does not seem annoyed by the fly. She is calm in describing the events that take place at death. 

The tone of the poem is calm, dreamy, almost completely relaxed, as if the speaker was floating away. We think that tone makes her sound just like a ghost...

The speaker's tone is so calm until death does not seem real. If it were not for the spectators, this point of death would be so serene until one would be surprised that any felt sadness enough to weep. 

The passage of death has an unsettling, disconnected tone but is not scary or painful. Death is painless. The stillness in the room creates a most peaceful passing. The tone is so calm until the reader does not get upset at the theme of death. Death is as natural as the buzzing of a fly. 

Describe the mood of the poem "I heard a Fly buzz—when I died—"

A person who recently died describes the scene at her deathbed in “I heard a Fly buzz—when I died—” The mood in the room is solemn and peaceful. Nonetheless, this calm atmosphere has an undertone of tension:

The Stillness in the Room
Was like the Stillness in the Air -
Between the Heaves of Storm -

The air is pregnant with sad suspense, as gathered onlookers expect death to arrive at any moment. Weeping mourners with bated breath convey a somber yet apprehensive mood:

The Eyes around - had wrung them dry -
And Breaths were gathering firm
For that last Onset - when the King
Be witnessed - in the Room -

The speaker’s family grieves and expects the impeding passing with both dread and hope. Bracing themselves for their loved one’s final breath, they also await God (“the King”) and watch for His presence in the sickroom. They believe that God (or the grim reaper some would say) is coming to take the dying person away.

With little sentimentality, the speaker notes that she has already prepared for death through practical arrangements. She has given away her “keepsakes” and whatever else she could, and then her speech is interrupted by a fly.

With Blue - uncertain - stumbling Buzz -
Between the light - and me -
And then the Windows failed - and then
I could not see to see -

A pesky fly buzzes around clumsily (“stumbling”), breaking the poem’s peaceful mood. Annoyingly buzzing between the speaker and the window—effectively blocking out light—the hapless insect deflates the somber and slightly tense mood. The event of the speaker’s death is matter-of-fact, not melodramatic or tragic. The interposition of the fly between the window and the dying person makes her death seem anticlimactic and quick: suddenly she cannot see daylight because of the fly, but she also no longer can see because she is no longer living.