Joseph McVicker was born in 1929 to Irma McVicker and Cleo McVicker. With Cleo McVicker's death in 1949, Irma McVicker hired her son, Joseph, and her son-in-law, Bill Rhodenbaugh, to head Kutol Products Company, a Cincinnati, Ohio firm, formerly headed by Cleo, that produced soap and wallpaper cleaner. Joseph McVicker soon realized that Kutol Products' wallpaper cleaner also could be used as a pliable modeling clay. In 1955, he tested the product in Cincinnati-area schools and daycares. The following year, the Woodward & Lothrop Department Store in Washington, D.C began to sell the clay, which McVicker had named Play-Doh. Joseph McVicker and his uncle, Noah McVicker, applied for a patent for Play-Doh in 1958, but the United States Patent Office did not officially patent the clay until January 26, 1965.

In 1956, Joseph McVicker and his uncle, Noah McVicker, created the Rainbow Crafts Company, Inc. The sole purpose of this company was to manufacture and sell Play-Doh. Originally Play-Doh came in 1.5 pound boxes and was an off-white color. The company also quickly offered red, yellow, and blue Play-Doh in gallon cans. Due to the large size of the packaging, the Rainbow Crafts Company began selling Play-Doh in eleven ounce packages. Kutol Products continued to manufacture soap and other cleaners, but Rainbow Crafts Company, Inc., became the sole manufacturer of Play-Doh.

In 1965, General Mills purchased the Rainbow Crafts Company, Inc., and all rights to Play-Doh. Joseph McVicker retired from his life as a businessman at this time. He was a millionaire at the time of his retirement. McVicker decided to become a minister and enrolled in Harvard Divinity School. He died in 1992.