D'Amico was selected by the Milwaukee Brewers in the first round of the 1993 Major League Baseball Draft. After three seasons in the minor leagues, he made his debut on June 28, 1996, and spent the next six years with the Brewers. After missing all of 1998 and most of 1999 due to shoulder surgery, D'Amico had a career year in 2000. That season, his ERA hovered around 2.00 for much of the season and he contended for the NL ERA title. Needing just a few innings to qualify for the title on his last start of the season, he surpassed the 162 inning minimum threshold, but in the process gave up enough runs to lose the title. D'Amico finished third, behind Kevin Brown and Randy Johnson.
D'Amico was never able to follow up that success, however, as he struggled with injuries for the Brewers in 2001, before ending his career with stints on the Mets, Pirates, and Indians. He led the National League in losses during the 2003 with the Pirates, and was released by the Indians in June 2004 after posting a 7.63 ERA in 7 starts for them.