Aceves uses a fastball, which can reach the mid 90s, a curveball, a changeup, and a cut fastball. He is known for his control and his ability to throw any pitch in any count.

Aceves was signed by the Toronto Blue Jays as an amateur free agent in 2001. He made ten starts in the Dominican Summer League that year. However, Aceves felt isolated, and when the Blue Jays assigned him to stay in the DSL for 2002, Aceves stayed in Mexico, and his contract was purchased by the Yucatán Leones of the Mexican League. Aceves pitched for Yucatán and Sultanes de Monterrey for the next six seasons.

Yankees scout Lee Sigman followed Aceves in the Mexican League, feeling he could achieve similar success as Teddy Higuera, who Sigman had signed for the Milwaukee Brewers. Feeling that he had developed well in the Mexican League, the Yankees purchased Aceves, along with Manny Banuelos and two other players, for $450,000 during the 2007–08 offseason. He began 2008 with the Single-A Advanced Tampa Yankees. He was quickly promoted to the Double-A Trenton Thunder and Triple-A Scranton/Wilkes-Barre Yankees. He was named Eastern League pitcher of the week for the week ending May 25, 2008.

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