The university plans to continue awarding degrees without "necessary expertise" to cope with the UK-wide industrial action.
But students fear their work which has taken months to complete will not be read.
The university dismissed the claim and said it had "robust measures" in place.
The boycott is the latest phase of industrial action by the members of the University and College Union (UCU) at 145 institutions across the UK.
The action began on Thursday 20 April and will continue until employers make an improved offer.
Union members are refusing to undertake marking duties, and assessment-related work such as exam invigilation or processing marks is also being avoided.
In response, universities are considering a number of measures including changing marking guidelines and basing final grades on work already submitted.
Ollie Lewis, who studies politics and works as a freelance journalist, spoke to students and staff about the issue for student paper the Edinburgh Tab.
He recently completed a 10,000-word dissertation, which he worries will not be read.
Mr Lewis told BBC Radio Scotland's Drivetime programme: "The idea of the boycott is that it would force the university to actually do something about this dispute and end the strikes because no one wants strikes for future year groups.
"But they haven't done that, they've decided to punish students instead and say 'we won't mark things you worked for months on'. It's an absolute disgrace to be honest."
Mr Lewis, whose dissertation took six months of work, said he knew students revising for exams who were unsure whether they would be marked.
Despite this, he said students were sympathetic towards tutors.
"I've been at university since 2019 so every single year I've had multiple weeks of industrial action," he said.
"I've spoken to students in recent days - the anger is not at staff, the anger is with the university.
"And that's because we've seen what staff have gone through to keep teaching us.
"I know tutors who have not been able to feed themselves properly because of the issues they're having with pay."
Staff recently spoke out against plans to award degrees at the University of Edinburgh without marking all of the students' coursework.
They said the response from senior management posed a "serious threat" to the integrity of its degrees.
The university said measures were in place to minimise disruption, and all student work will be read and marked.
About 500 staff signed an open letter to Edinburgh's senior leadership team which raised concerns around the impact on final year students, who may find a "large proportion" of their final assessments will not be counted towards their final degree.
Liberty Phelan is a fourth year English literature student at the University of Edinburgh. She handed in her two final essays and dissertation just after the marking boycott began.
She said her school representative informed students that the university was considering measures including relaxing credit requirements or not using a second examiner to verify coursework marks.
"Both would massively undermine the credibility of our degree," she said. "Especially if a huge chunk of our work isn't included.
"I recently submitted two essays and my dissertation, which is 16,000 words altogether.
"It's the culmination of all of my work throughout my degree and a meaningful piece of work for most people.
"It would undermine the credibility of the institution if such a large portion of our work wasn't included."
She said students were concerned they would not have their degree results in time to apply for further education or graduate jobs.
Ms Phelan said: "I have a lot of sympathy with staff as well, as we interact with them every day and they communicate with us about their tenuous contacts.
"A lot of students also want to work in academia but the current situation has put them off as it doesn't seem like a viable career path.
"The situation is also difficult for students because we have no recourse - we can't withhold our tuition fees as we've already paid them."
The University of Edinburgh said it had "robust measures" in place to reduce the impact of industrial action, and all students' assessments and work - including dissertations - will be read and marked.
A spokesperson said: "We are making every effort to provide results, degree award outcomes and progression decisions to students by the published timelines."
It said there were "temporary variations" in place to provide flexibility to marking assessments and "to ensure that academic standards are not compromised".
They added: "If there has been a significant enough disruption that the marking of assessments cannot be done in time, the University will provide an affected student with progression or degree results based on their marked work.
"The delayed additional results will be counted in a students' final mark.
"On the few instances where results are delayed, decisions will be revisited when additional results become available.
"At that time any previous award made will only be improved, not downgraded or rescinded."