Hi @bsrinvasan ,
I don't know of any way to set up Canvas to do this. But I have an idea that might work.
1) Create a "Category Total" assignment for each Assignment Group.
2) Add up all the individual assignment scores and put the total in the corresponding Category Total assignment.
3) Reset all the individual assignments to "Do not count this assignment towards the final grade." I think you can skip this step.
4) There will now be only 8 graded assignments that are counted (one per category), and you can drop the lowest of the 8 for each student.
ETA: Sorry, I realized you need one more step. You'll have to create ONE MORE Assignment Group with all 8 category "Grade Total" assignments in it and drop the lowest from there because the "drop" option appears to be attached to Assignment Groups. (I've never used this option and had to look it up.) So you'll have to make sure each Assignment Group has the same number of points since the traditional weighting by Group option will be useless. You'll have the 8 AGs containing the individual assignments; set all of those AGs to 0%. You'll have a 9th AG containing "dummy" assignments of the totals from each of the other 8 AGs. Set this Assignment Group to 100% and set a "rule" to drop the lowest.