Is there an Event when mouse goes off screen?

There is not, sadly. But there are properties of mouse titled X and Y, both represent positions of the mouse, both have contrary positioning purposes.

local m=game.Players.LocalPlayer:GetMouse()

while m and wait() do
    if m.X < 1 or m.Y < 1 then
        print('nope')
    end
end

This checks if the mouse is considered an outsider to the screen displayed.