It is interesting that you attach the adjective "deliberate" to the noun "cruelty." Whilst cruelty and violence is definitely a theme of the play, I am not so sure that we can say that they are "deliberate." Violence does however seem to be linked with sexual passion. Consider the way that violence is evident in the relationship of both Eunice and Steve Hubbell and Stella and Stanley. And yet it is the sexual element that makes this abuse "unimportant," in the words of Stella. Williams seems to be suggesting that domestic abuse is far more widespread than we would like to think, and meekly accepted by the woman in a relationship. However, it is uncertain whether the kind of violence that is alluded to can be called "deliberate" or whether it is just the result of anger or other strong emotions.
Certainly the central act of cruelty or violence in the play is what happens between Blanche and Stanley. It is interesting that when Stella shares what happens between her and Stanley with Blanche, she responds by saying what she is referring to is nothing more than "brutal desire." We can perhaps infer that somehow in Blanche's mixed-up past desire and violence have been linked, which explains how she almost goads Stanley into their final confrontation. Williams uses the characters of Blanche and Stanley to suggest that the cycle of violence, especially when it is mixed with desire and passion, can become repetitive and is difficult to escape.
Therefore I would agree that cruelty is a definite theme in this great play, however I would take issue with the word "deliberate." It is not clear whether the various acts of cruelty that are presented are the result of a deliberate choice or just a natural consequence of heightened emotions.