A cutting contest was a musical battle between various stride piano players from the 1920s to the 1940s, and to a lesser extent in improvisation contests on other jazz instruments during the swing era.
Up to the present time, the expression cutting in jazz is sometimes used, sometimes facetiously, to claim a new musician's technical superiority over another.
Cutting contests first had a more earnest meaning only among pianists, and later existed for their own sake. Originally, to "cut" another piano player meant to replace him at his job by outperforming him. This serious form of rivalry ended by the 1920s when pianists began acquiring more stable engagements, and basic ragtime and "fast shout" piano evolved into the more improvised stride style (a term that began to be used in the 1920s).
"Cutting" came to mean victory at a pre-arranged contest. These contests were usually held at Harlem home "rent parties", where an entrance fee helped residents pay their rent. In the contests, often one pianist began a tune; then others took turns "cutting in", introducing increasingly more complex ideas, changing the key and/or tempo, and otherwise trying to outplay and out-style the previous musician(s).
The great stride pianists James P. Johnson and his "rival", Willie "The Lion" Smith, often participated in cutting contests. However, they had so much respect for one another that their contests usually ended in draws, and they "cut in" only for humorous effect.
Cutting contests continued into the 1940s. Art Tatum usually won the contests he engaged in, beating out such notable pianists as Fats Waller, Teddy Wilson, Count Basie, Earl "Fatha" Hines, Albert Ammons, Harry Gibson, Pete Johnson, Marlowe, Clarence Profit, and Claude Hopkins.