There have been many different translations of Anton Chekhov's best short story, and some of them may have been cut or edited, but there was no need for any of them to be expurgated because the affair between Dmitri Gurov and Anna Sergeyevna never included any descriptions of nudity or physical intimacy. That sort of thing was just not done in literature at the time Chekhov was writing. Even the title has been translated in many different ways, including "The Lady with the Dog," "The Lady with the Pet Dog," and "The Lady with the Little Dog." 

If you are referring to the etext of the story in the enotes study guide, it appears to be uncut and an exact copy of the Constance Garnett translation. She has a sterling reputation as a translator of great Russian literature. According to Wikipedia:

Garnett was one of the first English translators of Leo Tolstoy, Fyodor Dostoyevsky and Anton Chekhov and introduced them on a wide basis to the English-speaking world.

It might seem to a modern reader that a story which is all about a prolonged illicit love affair should have more intimate descriptions, but this is only because modern readers have seen so much of of that sort of thing, not only in books but in movies, that it would seem almost obligatory. But in the nineteenth century and before, it would have been considered blatant pornography.

Further, according to Wikipedia:

Constance Garnett translated 71 volumes of Russian literary works, and her translations received high acclaim, from authors such as Joseph Conrad and D. H. Lawrence. Despite some complaints about being outdated, her translations are still being reprinted today (most also happen to be in the public domain).