Kolles warned immediately that the Leafield based team's 300-strong workforce could be shrunk by a third.
"Sometimes you have to make unpopular decisions," he told Reuters.
Indeed, it is believed many staff members were told on Monday and Tuesday that they are redundant.
Another departure, it became clear on Wednesday, is Rossi, who also drove for Caterham's GP2 team but will now not be in action this weekend at Hockenheim.
"Now it's time to move on," a statement on his Facebook page read on Wednesday.
"My goal is to be in F1 and add value to the sport and I'm very optimistic about my next steps; we have a great opportunity to grow the sport in the States and I believe the timing is perfect," Rossi added.
For the moment, it is believed Caterham's race drivers - Kamui Kobayashi and Marcus Ericsson - are safe at least for the forthcoming Hockenheim-Hungary double header.
But Kolles indicated there could be more changes coming.
"The last driver I sacked out of formula one was Christijan Albers," he said. "And he's my team principal. This should give you a taste of how I deal with people."