This incident can be found in Chapter Fourteen of this great novel, and is actually narrated to Nelly Dean by Heathcliff when he describes how Isabella foolishly decided to elope with him. Heathcliff spends some time how he finally managed to make his wife realise that he didn't love her and that he was not a "hero of romance." Notice how he did this from the very first moment she had agreed to elope with him:

She cannot accuse me of showing one bit of deceitful softness. The first thing she saw me do, on coming out of the Grange, was to hang up her little dog; and when she pleaded for it, the first words I uttered were a wish that I had the hanging of every being belonging to her, except on: possible she took that exception for herself.

The dog hanging incident therefore is a perfect example of the brutality of Heathcliff's character, and how he chose to marry Isabella only because it was part of his plot to gain revenge on Linton and have a chance of inheriting Thrushcross Grange. This is an excellent example of how he coldly and calculatingly uses other characters, treating them as little better than objects, to further his own goals.