I use the rubric feature to mark my assignments in speed grader, is there any way the the comments against each criterion along with the rubric can be downloaded in the feedback comments?
I don't believe this is possible from within Canvas itself, but if you have a bit of programming skill you could write some code using the Canvas API that pulls out all the submissions for a specific assignment then for each submission in the data that's returned you could see information including rubric comments, and display this in a table, spreadsheet etc.
Take a look at this recent post where another community member was asking about exporting assignment submissions and feedback. The aim here wasn't exactly the same as what you want - he was after text comments added in the SpeedGrader rather than rubric comments - but the method I described in my answer is similar to what would be used to get the rubric comments. The link I gave to the API documentation will also be relevant if you decide to try this for yourself.Export assignment comments for course
It might look a little complicated so if programming isn't your speciality you could ask your local Canvas administrator or another technical support colleague for assistance.
Retrieving data ...