If you're using the Canvas Integration, you can certainly assign-to specific students and exclude the remainder of the section(s) or students.
If you're delivering only via Mastery Connect, the easiest way to do that is to have the assessment (either a cloned version or different one if you want to assess using different questions) and provide the TEST ID specifically to the students who need to access it. If you are using the Student Portal, i would not enable it there as it will make it available to all students.
You can also delete/reset scores for a student if you wanted them to take the same assessment, however, I always recommend keeping original scores present for progress and growth monitoring.