I use Windows 8.1 and even though I choose not to upgrade to Windows 10, i keep seeing the Windows 10 Upgrade icon on my computer and it is frankly annoying. Is it possible to remove it completely ? Also, can this icon slow down my PC ?

Do not worry, this executable cannot bring harm to your PC. In fact it takes around 0.03% of your CPU Power. But yes, for users who do not want to upgrade, it can be quite annoying.
It is associated with the update KB3035583 and it runs an executable in your Windows Task Manager going by the name of GWX.exe. To remove it, go to Windows Update from Control Panel, then:
1)Go to Installed Updates from the bottom left corner of the screen.
2)A window similar to Programs and Features will appear. Locate "Update for Microsoft Windows (KB3035583)", mark it with your mouse and then click on Uninstall.
3)Restart your PC and you should be fine.

You are welcome   

I just want to make a note, that this KB3035583 update is a recurring one! I keep marking it with the "Hide update" feature and it keeps coming back - 4 or 5 times now!   
So, my suggestion is to not run Automatic updates, and keep checking for it in the "Installed updates" section and for the GWX icon.

@Sabrina, I also upgrade window 8.1 to win 10 but after 2 to 3 days revert back to win 8.1 because my laptop touch screen doesn't work on win 10.