Asham, who was offered an in-person hearing, was assessed a first-period match penalty for cross-checking Brayden Schenn around the chin and punching him in the head when Schenn was down.
Neal had two separate hearings with NHL disciplinarian Brendan Shanahan on Tuesday - one for his third period hit on Flyers rookie Sean Couturier and the other for a hit to the head on Flyers forward Claude Giroux. He was given a charging penalty for the latter hit, which saw four players - including Neal - receive 10-minute misconduct penalties.
Neal, who shares the team lead in playoff scoring with two goals and five points - is a repeat offender. He was suspended two games last season for a hit from behind on Derek Dorsett and was fined $2,500 this season for a high-stick to Montreal's P.K. Subban.
Neal will miss Game 4 on Wednesday night. Penguins will also be without forward Craig Adams, who received an automatic one-game suspension from the NHL on Monday for instigating a fight late in Game 3.