Cuevas, who entered the clay-court tournament ranked No. 107 in the world, advanced to his second semifinal of the year after beating the 14th-seeded Spaniard. Cuevas beat another seeded player in the third round, No. 8 Philipp Kohlschreiber.
The 23-year-old Uruguayan's biggest success so far was winning the French Open doubles title in 2008 with Luis Horna of Peru.
Almagro had beaten French Open runner-up Robin Soderling in the previous round.
Cuevas next meets 13th-seeded Paul-Henri Matthieu, who advanced to the semifinals when Viktor Troicki retired in the first set with a foot injury. Matthieu was leading 3-0.
Fabiano’s agent questions offerSchiavone advances to 2nd round in Prague
