The mood is unremittingly bitter, bleak, harsh and unpleasant, showing in viscerally thick verbal detail the absolute horror endured by the men who fought in World War 1.
Within that, though, I think there a few separate moods in the various stanzas of the poem. The first stanza is heavy, tired, almost asleep with weariness, and the rhythms drop in heavily, slowly, painfully...
All went lame; all blind;
Drunk with fatigue; deaf even to the hoots
Of tired, outstripped Five-Nines that dropped behind.
Then, as the gas explodes, the poem picks up pace and the mood becomes one of terrified, gasping panic:
Gas! Gas! Quick, boys! – An ecstasy of fumbling, Fitting the clumsy helmets just in time...
There's then another painfully bloody and gruesome description of a man dying from gas, and the mood is almost wincingly painful, emphasising little details. And the final stanza then changes into a new, more angry, more ironic mode: the mood is aggressive, hostile to the reader, and it hammers home its final ironic point:
You would not tell...
The old Lie; Dulce et Decorum est
Pro patria mori.
An exceptional, wonderful poem, I think. Hope it helps!