One victim told a court she found herself on the ground with the attacker's fist raised above her.

The man, a Bangladeshi, 29, was carrying a knife when he was arrested less than a week after arriving on a student visa.

Federal authorities said he could not be deported because he did not fail the nation's character test.

He is living in Melbourne's western suburbs.

When he faced Sunshine Magistrates' Court last month he was placed on a 12-month community-based order on charges of robbery, possessing a controlled weapon without an excuse and theft.

He was also ordered to complete an anger management course. No conviction was recorded.

The victim was walking to Albion railway station at peak hour when the man approached from behind, grabbed her by the shoulder and punched her to the ground as he tried to snatch her handbag.

"When I was on the ground, he still tried to steal my bag, and he then raised his fist to try and punch me. Once he did this, I did not resist and he took my bag," the woman said.

"(It) was absolutely horrendous and frightening - as it happened in proximity of my street, and also happened in peak hour."

The victim said police told her they expected the man to be deported.

"But it does not surprise me that this has not occurred," she said.

"It appears that you need to commit murder in Australia before that is considered. I think it's pathetic that this man who has terrorised hard-working Australians is allowed to remain in this country, but again ... it's not surprising."

The other victim also lost her handbag to the thief near Albion railway station two days earlier.

Victoria Police confirmed it had moved to have the man's visa cancelled.

"As part of the investigation and court proceedings, Sunshine CIU detectives applied to the Department of Immigration for the offender to be deported," a police spokeswoman said

An Immigration spokesman said that among reasons for failing the character test were having a substantial criminal record, such as being sentenced to a year's jail or more.