***** NOT A TEACHER *****
Here is some information that may interest you:
"When we wish to show that some action was performed ... by somebody else at our instigation [our orders], we use the
verb to have and the past participle."
The book's example: I have + my shoes + shined + (by someone).
Then the book says: "The participle ... is really [in reality] a passive infinitive with to be suppressed [not said]."
Thus, your quoted sentence seems to be:
The leader + is having + senior generals + (to be) executed + (by mortar fire).
IF my analysis is correct, all the the credit goes to Practice Exercises in Everyday English For Advanced Foreign Students
by Robert J. Dixson, pages 156 -157 in the 1957 edition.