Aspinall averaged more than 107 in a professional display, dropping just one leg as he booked a third-round meeting with Ross Smith.
"People keep thinking I've retired," Aspinall joked after his match.
"Mickey played well, but I felt so relaxed tonight. I think the thought of watching England (in the FIFA World Cup) later made me relax.
"It’s a great win, and I’m looking forward to tomorrow (Sunday).
"I knew I had a tough game in Mickey. He plays his way, but it didn’t affect me. I’m just very happy with the win.”
Schmidt, who fought back from 5-1 down to beat Cameron Menzies on Friday, followed it up by edging past Belgium's Mike De Decker in a deciding leg to continue the best run of his career.
"I will take what I get. For me, it’s not important who my opponent is," Schmidt said.
"I try to play my game; I play against the best players in the world, and we’ll see tomorrow."
The 21-year-old will now face James Wade, who defeated Maik Kuivenhoven 6-4.
Top seed Gian van Veen opened his campaign with a 6-3 victory over home favourite Niko Springer, as Krzysztof Ratajski beat Max Hopp to earn a meeting with the Dutchman.
Luke Woodhouse and Jermaine Wattimena both progressed without dropping a leg, defeating Dragutin Horvat and Kim Huybrechts, respectively.
Jonny Clayton eased past Karel Sedlacek to set up a meeting with Woodhouse, while Ryan Joyce overcame Stephen Bunting to book a tie against Wattimena.
Elsewhere, ProTour leader Wessel Nijman whitewashed Bradley Brooks to set up an all-Dutch clash with Dirk van Duijvenbode, who beat Chris Dobey 6-2.
Michael van Gerwen also advanced, producing vintage finishes of 142 and 130 in a 6-2 win over Joe Cullen to earn a meeting with Damon Heta. Kevin Doets defeated Martin Schindler to complete the last-16 line-up.
Results
Round two - afternoon
Damon Heta 6-4 Rob Owen
Jan Schmidt 6-5 Mike De Decker
Luke Woodhouse 6-0 Dragutin Horvat
Sebastian Bialecki 6-3 Danny Noppert
Jermaine Wattimena 6-0 Kim Huybrechts
Dirk van Duijvenbode 6-2 Chris Dobey
Wessel Nijman 6-0 Bradley Brooks
Krzysztof Ratajski 6-3 Max Hopp
Round two - evening
Ryan Joyce 6-4 Stephen Bunting
James Wade 6-4 Maik Kuivenhoven
Jonny Clayton 6-1 Karel Sedlacek
Michael van Gerwen 6-2 Joe Cullen
Gian van Veen 6-3 Niko Springer
Kevin Doets 6-3 Martin Schindler
Nathan Aspinall 6-1 Mickey Mansell
Ross Smith 6-1 Niels Zonneveld