‘Good-morning; good-morning!' the General said
When we met him last week on our way to the line.
Now the soldiers he smiled at are most of 'em dead,
And we're cursing his staff for incompetent swine.
‘He's a cheery old card,' grunted Harry to Jack
As they slogged up to Arras with rifle and pack.
But he did for them both by his plan of attack.
Here Sassoon states unequivocally that the General is responsible for the deaths of the soldiers.  The dark comedy doesn’t alter the fact that the General is a buffoon, and a tragically dangerous one. 
 Note the rhyme fits with the last two lines of the previous stanza, stressing the satire further.
The General