The Austin Powers thing didn't really spoof Mission Impossible...it was just your typical over the top Hollywood wham-bang action movie version of what a Powers movie would be like if Austin was real and they made one out of his adventures. Everything was hyper-real in that, and the Cruise/Paltrow casting was simply because they were the biggest celebrities at the time.
I don't think it was spoofing M:I-2 per se, but just that general genre. They did a good - and very funny - job!
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As for the original Mission series, the basic concept was that Peter Graves was a top operative who would assemble a new team each week (though often using many of the same "trusted" faces) and they'd pull off the impossible mission.
With Brian ("I wanna be an art-house Hitchcock but need a hit movie so I'll do this for the money!") De Palma's first film, they completely ruined Graves' Jim Phelps character (after all those years of service, he's going to jack it in like that? No, siree) and turned it into essentially a James Bond franchise for Cruise to look good in.
The sequel was an insult to audiences and fans of the show (and even the first film), with a comeback for Ving Rhames character purely based on his "cool factor" popularity. The middle saaaaaaaaagged badly, and all the other action moments were literally ripped off and pulled from other movies (Cliffhanger, T2 and director John Woo's own catalog of over used cliches such as the flying doves, slow-mo, and hand-to-hand fisticuffs on a beach that just went on. For. Ever.).
As for Cruise saying he wanted each one to be different, with different directorial styles, well, that plan seems to be out the window. David Fincher was attached for a while to III (how cool would that have been!?!) but dropped out only to be replaced by the anemic Abrams, who essentially gives us a re-hash of the first film, masked with over glossed locations and explosions that try - but fail - to hide the plot holes.
Mission aborted...let this movie self destruct in five seconds!