1
general::
Excuse oneself without giving the real reason for leaving, especially to go to the toilet or have an alcoholic drink. For example, Excuse me, I have to see a man about a dog. This euphemistic term dates from the Prohibition days of the 1920s, when buying liquor was illegal, and, after repeal, was transferred to other circumstances.
American Heritage Idioms
2
general::
Phrase(s): see a man about a dog
Fig. to leave for some unmentioned purpose. (Often refers to going to the rest room.) • I don’t know where Tom went. He said he had to see a man about a dog. • When John said he was going to see a man about a dog, I thought he would be gone for only a minute.
McGrawhill's American Idioms And Phrasal Verbs