It might also be worth seeing some youtube videos to get a sense of what other people with a 1060 3gb are getting gameplay wise. It seems like what is happening is the frame rate must be suffering a major drop when looking around.

Hoggle:  I will see if just standing and looking left and right if my frame rates are dropping if they are its not much .
Ty_ger07:  That is something I need to look at. No I only have Destiny 2 right now but I have COD all versions and Battlefield 3 and 4 and some others but the download is so huge and takes forever but ya I probably should install one and see. I just wonder would a full GTX 1060 6gb be any better ? I would hate to spend 2 or 3 hundred dollars and find out it did not fix the problem.

Turn off TXAA if its available.
 
Otherwise just accept the limitations of your LCD monitor,  the only ones that don't  blur during movement are those runningin lightboost/ulmb mode.

Hi Squall: My monitor I really doubt that it has an issue it is a brand new Asus VG248QE 1ms response time @ 144hz I have tried any number of resolutions and a number of hz 144,80,60 same issue.
I am try to load it on a intel machine to see if its the GTX 1060 card,,, IDK its should not be this much trouble to run a stupid game in 2018.

it doesn't matter how fast the response time is, because of our eyes retaining light information till it changes, we see blur on as the lcd crystals change.

So no matter what graphics card I have were going to get blurring left to right mouse movement ? Nothing else blurs: ridding a sparrow, sprinting, just left right even slow moving mouse IDK.

Do you know what you should do?  You should install a different game and compare.

Yes ty_ger07 my only issue there is I only have a 250gb SSD and most games today are 35 to 70+ gb  so its hard to work out the space right now. I wish someone had a demo that would test mouse movements in a game that I could download and test it, something other than just a demo telling me how many fps im getting.

I know this post is 6 years old, but I was wondering if any solution has been found? As I am struggling with the same problem and have spent countless hours changing settings, uninstalling/reinstalling programs, and the only thing I have found so far to fix the blurring issue when moving is to wipe my system and completely reinstall windows!
 I don't completely understand why it is happening as it seems random as to when it does happen, take last night for example friends and I were playing for hours with no issues and when I jumped back in this morning it was blurring when I move and there were no updates or changes to the system and the only game it seems to happen to is Destiny 2.
 If anyone has any updated info on this or can point me to a thread that does it would be greatly appreciated, Thaniks!