"Harsh" implies that something is strong and possibly painful. For example, a teacher my harshly critique your writing. There is no intention on the teacher's part to cause you pain (even though you may feel sad or hurt that there are corrections all over your paper, and you received a D). A harsh punishment is generally a strong punishment but generally not considered excessive.
"Brutal" implies that something is excessive and is usually painful. For example, a brutal criticism (unlike a harsh criticism) probably goes beyond just correcting mistakes. A brutal criticism may attack the person as well (ex. "This writing is idiotic" instead of "This sentence is grammatically incorrect.") Generally something that is brutal is often painful or causes pain. A workout can be brutal if at the end of it you're exhausted and sore for the next few days, but a workout wouldn't be harsh. If you're familiar with Game of Thrones, then the winters in the north are brutal. (You may be able to say the winters in the south are harsh. The winters in the north are more extreme than the ones in the south.)
"Cruel" generally implies that something was done to cause pain intentionally. A cruel criticism would leave the author of a paper feeling worthless (much as a brutal criticism might), but a cruel criticism implies that the critique wanted to inflict pain and suffering on the author. Someone who deals out a cruel punishment delights in seeing the pain that results. Continuing on the Game of Thrones theme, Joffrey is a cruel character.
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