The 18-times grand slam champion, whose last title at Halle was in 2015, skipped the entire claycourt season after winning the Australian Open and claiming titles at Indian Wells and Miami this year, to prepare for grass.
He will face rapidly rising talent Karen Khachanov, who won his all-Russian quarter-final against Andrey Rublev 7-6(8) 4-6 6-3 to reach his first tour semi-final of the year.
"It was important to be aggressive off the baseline and make him feel my variation and the power I can bring to the court," Federer said.
"I think I did it very well. I had lots of chances to even go up a double break in the second set."
"I thought I was very calm out there, even in difficult moments. I was calm serving out the first and second sets. Those are always signs for me that things are slowly starting to fall into place nicely."
Federer, who has yet to drop a set in Halle after losing in Stuttgart in his first match back last week, limited his serve-and-volley game against the German who is a fine returner and Mayer was broken quickly as his opponent won the first set.
The 33-year-old Mayer squandered two break-points at 1-0 in the second set and paid the price as Federer broke again and never relinquished his advantage to win in just over an hour.
Frenchman Richard Gasquet also reached the last four, edging past Dutchman Robin Haase, who had eliminated second seed Dominic Thiem in the previous round, 6-1 3-6 6-1 and looked to be hitting top grasscourt form at just the right time.
Gasquet will next play Germany's Alexander Zverev, last year's finalist who has won three titles this season, after he muscled past baseliner Roberto Bautista-Agut 6-7(6) 7-6(1) 6-1.
The pair held serve for almost two hours before Zverev managed the first break of the match early in the third set and the 20-year-old broke again two games later to finish the Spaniard off.
(Reporting by Karolos Grohmann; Editing by Ed Osmond)
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