Robert Penner, 38, had been working in Nepal for nearly four years when the country's immigration department said on Tuesday he had violated the terms of his visa and gave him two days to leave.
Penner's lawyer had approached the Supreme Court to stay the government's decision pending an appeal, but his time ran out before the court heard the case.
"Our case was scheduled for today but we did not get a turn," lawyer Dipendra Jha told AFP.
Penner had spoken out on a number of controversial issues, including a new national constitution that sparked deadly protests last year.
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He recently tweeted criticism of the country's anti-corruption watchdog for its handling of the arrest of a Nepali magazine publisher and editor who has since been freed on the orders of the Supreme Court.
The immigration department said he had violated the terms of his visa by "commenting on internal matters of the country, inciting conflict and disturbing social harmony."
Penner had been working in Nepal for the technology outsourcing company CloudFactory, which said on Wednesday it had decided to "discontinue" his employment.
"His cancellation of visa over tweets is arbitrary. It is not suitable for a democratic country," said Jha.