I have been accepted to go to college in Montreal, but was told I could not work there because they only issue either a student visa or a work visa at one time. Is this correct? Are there any ways around this?

Not true, there are Student work visa's, but it is the school's choice whether or not to participate in this. The school would have to help you find an on or off campus job, check the link below, at the bottom of the page there is a link to a list of schools that participate in combined student/work visa's.

You are limited to 20 hours a week of work though.

Studying in Canada: Work Permits for Students - Working Off Campus