I guess satellite internet? Or maybe the mobile only cut the voice and it didn't occur to them that significant use could be made of SMS?
The article seems a bit hyper. "As the regime shut down other forms of communication, Twitter survived." - does Sullivan think Twitter has some uniquely resilient technology? Twitter will survive right until whoever's in charge takes the 10 seconds to put twitter.com into Iran's blocked sites list (or, you know, the next the fail whale)
But in a country where people live on roughly $2 a day (http://www.guardian.co.uk/world/2001/sep/25/afghanistan.terr...) I doubt many have $1,400 satellite phones that cost $6 a day to use.
Other methods are impossible...
Twitter is blocked through regular internet (see Michael C. McHugh comment here: http://www.politico.com/blogs/bensmith/0609/The_stakes_in_Ir... )
Cell phone towers are what's been cut so no SMS (http://www.google.com/hostednews/afp/article/ALeqM5jSPlmVgh-...)
Satellite dishes have been banned since '94 (http://ipsnews.net/news.asp?idnews=34407) so no highspeed internet that way.
I believe there was an article in the NY Times about this exact issue. Everybody "middle-class" and up has a satellite dish. Every few months the government confiscates them, at which point everybody goes to the local black market dealer, buys a new one and puts it back up. Quite often the new one is their old one because usually the black market dealer is whoever is in charge of the local branch of the satellite dish confiscation agency.
Ah, reminds me of the bad old days in the Soviet Union.