how to add damaging to this new instance?

All you would need to do is use the variable you set for the part and connect the touched event to deal damage. That would make your script look like this:

local tool = script.Parent
local mouse
local debounce = false 
local dmg = --set damage here

tool.Equipped:Connect(function(m)
    mouse = m
end)

tool.Activated:Connect(function()
    if mouse then
        local Part = Instance.new("Part",workspace)
        Part.Position = script.parent.Handle.Position
        Part.Material = Enum.Material.Neon
        Part.Size = Vector3.new(0.5,0.5,0.5)
        Part.CanCollide = false
        Part.Anchored = true
	
	Part.Touched:Connect(function(hit)
		local h = hit.Parent:FindFirstChild("Humanoid")
		if h then
			debounce = true
			h:TakeDamage(dmg)
			wait(1)
		end
		debounce = false
	end)
    end
end)

I did a little more than adding touched. One thing I did was add debounce so that the part could only deal damage once every second. The second thing I did was add a variable named "dmg" so you could easily change how much damage the part deals. Hope this helped!