Aspinall produced an outstanding performance, averaging 105.15 - the fourth-highest average ever recorded in the World Grand Prix's demanding double-start format.
Despite the straight-sets defeat, Joyce twice forced the world number 15 to go the full distance within sets. Aspinall ultimately prevailed with a 47% checkout rate, hitting nine of his 19 attempts to book his place in the last four.
Wade brilliant, Price nerveless
Gerwyn Price was given a far tougher examination by fellow Welshman Jonny Clayton, recovering from 2-0 down before edging a close deciding contest.
Price levelled the match with a series of solid legs but again found himself 0-2 behind in the deciding set. Clayton then missed match darts and Price took advantage to complete the comeback.
Price will now face Aspinall for a place in the final, with the Englishman likely to be a slight favourite after his performance on Friday.
James Wade was far more convincing. He has lost just one match since the end of August and was in commanding form again, beating Gian van Veen 3-0 while surrendering only one leg.
Van Veen averaged 81.56 as Wade moved through in comfortable fashion and now appears to be on a par with Luke Humphries ahead of Saturday's clash.
Humphries faced the surprise quarter-finalist Niels Zonneveld, who had already beaten Josh Rock and Gary Anderson. But Humphries proved a step too far for the Dutchman.
Despite some solid scoring, Zonneveld lacked the necessary timing against the experienced Englishman. The turning point came when he missed a dart to win a leg in the second set, with Humphries responding with a 75 checkout before completing the 3-0 victory.