humanoid is not a valid member of model?

There are few issues with your script. First of all, when you are cloning the dummy, instead of parenting the clone (copy), you are parenting the template. Correct code should look like this:

        pdummy:Destroy()
        copy = spdummy:clone()
        copy.Parent = game.Workspace["respawning dummy 1"]
        pdummy = copy --copy is now the new dummy

Now the more serious problem. Your click detector connection is still connected to the old (now destroyed) dummy. You have to make a new connection everytime a new dummy appears. So your whole script should look like this:

local pdummy = game.Workspace["respawning dummy 1"]["Player Dummy"]

local spdummy = game.ServerStorage["Player Dummy"]

local clickdetector = game.Workspace["respawning dummy 1"]["Player Dummy"]["HumanoidRootPart"]["ClickDetector"]


local function OnClick() --name your function, so you can reuse it
    pdummy.Torso.WeldConstraint.Enabled = false
    pdummy.Head.WeldConstraint.Enabled = false
    pdummy["Left Leg"].WeldConstraint.Enabled = false
    pdummy["Right Leg"].WeldConstraint.Enabled = false
    pdummy["Left Arm"].WeldConstraint.Enabled = false
    pdummy["Right Arm"].WeldConstraint.Enabled = false

    wait(0.1)

    local explosion = Instance.new("Explosion",pdummy)
    explosion.BlastRadius = 5
    explosion.ExplosionType = Enum.ExplosionType.NoCraters
    explosion.Position = pdummy.Torso.Position
    explosion.BlastPressure = 500000
    explosion.DestroyJointRadiusPercent = 0
    pdummy.Head.oof.Playing = true
    pdummy.Humanoid.Health = 0

    wait (2)


end

clickdetector.MouseClick:Connect (OnClick) --connect here

while true do
    wait(5)
    if pdummy.Humanoid.Health == 0 then

        pdummy:Destroy()
        copy = spdummy:clone()
        copy.Parent = game.Workspace["respawning dummy 1"]
        pdummy = copy
	--make the new connection
	clickdetector = pdummy["HumanoidRootPart"]["ClickDetector"] --click detector from the new clone
	clickdetector.MouseClick:Connect (OnClick) -- connect clone (copy) clickdetector
			

        end

Have a nice scripting session!

EDIT: BTW, do not worry about disconnecting the old connection as server will do that automatically during Destroy() function.