Black Comedy is all about the manipulation and exploitation of the tragic, for comic effect. They don't necessarily need to be about cruelty, though its often a contributing factor in many cases.
Consider Catch 22 for example, a quintessential Black Comedy text. The tragic nature of war and its effects on the individual are reduced to comedy, through hyperbole and the ridiculous farcial presentation of events. While the content is tragic, the effect is humorous. Hence, Black Comedy.
All that being said, what is the text you are studying?