I have this part that has virtually no flat surface on it. I am able to modify it to my needs up until i have to create a groove cut of 1mm wide and 1mm deep (see Capture 2). Im able to create the sketch and use the projected curve sketch but when i try to extrude cut, it cuts the entire sketch instead of just the groove (see Capture). What am I doing wrong? Is there another approach to this?
I'm on 2018, your file is a future version. You could post an iges or step, but I'd lose any sketch or relations and such things I think and would not be able to help you. I think some issue(s) you're having are at that level and someone else with 2019 would need to view your file to confirm and to correct at the sketch or feature profile type level.
What you want can be done to make this groove. Your groove sketch can be planar, using off-set surface as an end condition. To help in avoiding any small gaps or issues like this at the sketch or curve level path that you're going down.
..I'll add to what Jesse said,.. since I also do not have 2019.. I import/export via fusion360 to get a dumb file and noted this data has two face errors (file image -za).. I'd suggest you make sure you have VOR on and also run a Tools/Evaluate/Check to locate and repair any issues.
The workaround,.. I can do a Surface Cut.. although, it still has the underlaying face errors. (file - zb)
It may seem that is the issue. The file given to me has those surface issues that is confusing solidworks. I found a tedious but another approach. I created a "cutter"
with a round feature to help me locate it with my original part. I then mated them accordingly and edit the extrude feature in the assembly by changing Blind to Up to the Surface. 
I then opened each part separately to break their external references. Once I broke it, I went back to the assembly and re-mate the parts with 1mm into the part. I then used the Cavity feature to cut my part:
Hope this can help others and thanks for the feedback!
..I'll add to what Jesse said,.. since I also do not have 2019.. I import/export via fusion360 to get a dumb file and noted this data has two face errors (file image -za).. I'd suggest you make sure you have VOR on and also run a Tools/Evaluate/Check to locate and repair any issues.
The workaround,.. I can do a Surface Cut.. although, it still has the underlaying face errors. (file - zb)