Sasic netted three times in the first half against a hapless Ivory Coast side who had goalkeeper Dominique Thiamale to thank for preventing an even worse defeat. Mittag scored another two before half-time.
Top-ranked Germany, who won all 10 of their qualifying matches with a staggering 62-4 goal difference, came into the tournament as one of the favourites and showed why against woeful debutants Ivory Coast, who are ranked a lowly 67th.
Ivory Coast adopted an inept offside trap right from the start and stuck to it in the first half, despite German players regularly steaming through to score.
"It was nice, we scored a lot of goals. I'd be lying if I said it wasn't fun," said Mittag.
The Germans took off Sasic at half-time but were still far too strong. Mittag netted Germany's sixth goal after a terrible error in the Ivory Coast defence while Simone Laudehr, Sara Daebritz, Melanie Behringer and Alexandra Popp also scored.
"We just took the wind out of their wings and they lost their energy and we just kept going," said German coach Silvia Neid.
The heaviest defeat in Women's World Cup history came in 2007, when Germany beat Argentina 11-0.
Only a string of excellent saves from Thiamale and some lazy finishing prevented Neid's side from racking up a record.
Ivory Coast coach Clementine Toure refused to be downcast, praising her goalkeeper and saying the players would benefit from the experience.
"We have to ignore the score and the negative points ... we were playing the best team in the world," she told reporters.
The Germans, who won the World Cup in 2003 and 2007, are looking to make up for the disappointment they suffered when they hosted the tournament in 2011, losing to Japan in the quarter-finals.
Germany are now top of Group B, ahead of Norway, who earlier beat Thailand 4-0. They meet Norway on June 11 in a game that will decide who tops the group.
(Reporting by David Ljunggren, editing by Gene Cherry)
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