How do I set only the Orientation of a CFrame?

As far as I understand, a CFrame can generally be broken down like this: CFrame.new(Vector3 pos, Vector3 lookAt) My last question was about using welding to allow for rotation, which I solved using constraints. I needed to allow rotation because I want a gun to point at the mouse (think Metroid Prime). Here's my code:

wait(2)
playerTable = game.Players:GetChildren()
player = playerTable[1]
print(player)
mouse = player:GetMouse()
att = Instance.new("Attachment")
att.Parent = player.Character["Right Arm"]
con = script.Parent.GunCon
con.Attachment1 = att
con.Attachment0 = script.Parent.Attachment
wait(10)
while true do
	wait()
	script.Parent.CFrame = CFrame.new()--, mouse.Hit.p)
end

If I set the position vector3 of the CFrame, it constantly messes with the position of the gun, as to be expected; however, I need to access the second argument of the CFrame without accessing the first. I want to leave the position be and use mouse.Hit.p as the orientation. I hope that makes sense. Thanks.

Fundamentals

I don't think you understand the full potential of CFrame. Passing a position and direction vector to CFrame is only one of several different CFrame constructors. No matter what constructor you use, your CFrame value will always have the same parameters: PositionX, PositionY, PositionZ, Rotation00, Rotation01, Rotation02, Rotation10, Rotation11, Rotation12, Rotation20, Rotation21, Rotation22 (in that order).

The first three arguments make up the 3D position for the CFrame, and last nine arguments comprise the rotation matrix. Now you see why there are different CFrame constructors, keeping track of each element in the rotation matrix every time you wanted to rotate something could get a bit complicated.

Position and rotation are different

Position and rotation have no direct correlation with each other. You can change one without it effecting the other (just make sure the constructor allows for it). If you wanted to change the position without changing the rotation, here are a few examples...

Converting Rotation vector to radians

-- Converting all vector dimensions to radians for the CFrame.Angles constructor
local partRot = part.Rotation
local rad = math.rad

part.CFrame = CFrame.new(x, y, z) * CFrame.Angles(rad(partRot.X), rad(partRot.Y), rad(partRot.Z))

Using CFrame components to extract the rotation matrix

-- Gets the arguments after the 4th position, which is the rotation matrix.
part.CFrame = CFrame.new(x, y, z, select(4, part.CFrame:components()))

If you wanted to change rotation without modifying position, here is an example...

-- Creating a new CFrame with a position with an empty rotation matrix, then filling it by using CFrame.Angles
part.CFrame = CFrame.new(part.Position) * CFrame.Angles(x, y, z)

There are always several ways to do the same thing, some options are better than others depending on what you're doing. Anyways, hope this helped clear things up a bit. Let me know if you have any questions.