Is there a way for me to get to Greenland from Canada without flying? Basically I'm looking for it to be as cheap as possible.
According to Visit Greenland, at the time of writing there are no ferries to Greenland from either Canada nor Iceland nor Denmark. Indeed Greenland doesn't seem to be an appealing market for inter-country ferries. The linked site nevertheless suggests hopping on a cruise that includes Greenland on its list of destinations, as these are becoming more and more popular. Quoting from Visit Greenland:
By sea to Greenland
There are no ferry connections between Greenland and Iceland, Denmark or Canada. However, more and more cruise shipping companies are choosing to include Greenland on their itineraries, whereby it is possible to begin the voyage from Iceland or go onboard at, for example, Kangerlussuaq. Some shipping companies also sail from the USA and Canada or a country in Europe.
Note that the country itself does have quite a well developed coastal ferry system that takes you from port to port. There are just no ferries to/from other countries to date.