The ex-SNP member for Kirkcaldy and Cowdenbeath said he and his staff lived in fear during the hate campaign, just six months after the murder of Jo Cox MP by a far-right terrorist.
Mr Mullin, 69, who lost his seat in the June 2017 general election, was speaking after Shri Devi Hailes - also known as James Wells - was convicted at Kirkcaldy Sheriff Court.
The charge against Hailes, 54, said the emails, which were sent between December 3, 2016, and January 3, 2017, included menacing and threatening remarks and that the conduct of the accused caused Mr Mullin fear and alarm.
He was told he would “pay for your ignorance” in one of numerous disturbing emails.
He added: “It was disturbing for me and my staff. He said he knew where we were, our movements and that we had nowhere to hide.
“He claimed to have a military background and the threats were escalating.”
Mr Mullin said he was reluctant to report the incident, but took the advice from House of Commons officials to notify the police, who he praised along with prosecutors for their handling of the case.
Hailes was convicted at Kirkcaldy Sheriff Court on January 30 and will return for sentencing on March 14.
“I am not a medical expert but this person seemed mentally disturbed and I was reluctant to get the authorities involved,” said Mr Mullin.
“Society has a duty of care to those with mental health problems, but I also have a duty of care to my staff.
“I have no desire for revenge or punishment and I hope he gets the support he needs.”
The events happened six months after the murder of Jo Cox MP, who was shot and stabbed in her constituency by a far-right terrorist in June 2016.
Mr Mullin said MPs are vulnerable by the nature of their job, but insisted they must remain accessible to the public.
“It’s difficult to know where to draw the line,” he said.
“I’ve always been of the firm belief that MPs should be as open and available to the public as possible, but in doing we are putting them and their staff at risk.
“That’s unfortunately the way society has gone right now.”