“Ay-ay-ay” is an exclamation which entered American pop culture from Mexican Spanish in various ways. In informal conversation, the phrase means literally “oh, oh, oh” and conveys a sense of dismay.
For example, in 1882, the popular song “Cielito Lindo” included this phrase in the chorus. This song was sung by drunk mice in a Warner Brothers cartoon featuring Speedy Gonzales aired since the 1950s. It was also sung by the mascot of Fritos corn chips, the Frito Bandito, in a popular television commercial aired from 1967 to 1971. (Both characters, incidentally, were voiced by voice actor Mel Blanc.)
Closely related in sound is the exclamation known as the “Grito Mexicano” or “Mexican Cry”.