They were elected based on their promise not to accept more austerity. I would agree with parent that they don't have a democratic mandate to do the opposite now, even if they could legally do it.
A mandate is an authorisation to do something, not an open-ended power. The rest of that quoteed phrase references what the mandate was about - they were elected on a campaign to do the opposite course of action.
Then whats the point of the referendum. If they insist on non-austerity, make a plan outside the euro.