Yes, you can make group-specific discussions in Canvas.  You will need to create the student groups prior to creating the group discussions.

Further resources:

• How do I create a group discussion in a course?
• How do I assign a graded discussion to a course group?
• How do I assign a graded discussion to an individual student or course section?
• How do I add a group set in a course? 
• How do I automatically create groups in a group set?