Making the head of a character... the only thing?

That sounds like an interesting game idea! Here is a script in detail :)

Script: (Make sure the script is a ServerScript inside ServerScriptService)

local plr = game:GetService("Players")  --[ Defines the Player Service.

local function invis(char)  --[ Invisiblilty Function
    for a,b in pairs(char:GetChildren()) do  --[ Gets all children of the player's character.
        if b:IsA("MeshPart") and b.Name ~= 'Head' or b:IsA("BasePart") and b.Name ~= 'Head'  then  --[ Checks if the part is a Part and  not the head
            b.Transparency = 1 --[ Transparent 
            b.CanCollide = false --[ No Collisiosns
        end
    end
end

plr.PlayerAdded:Connect(function(player)  --[ Runs when player is added
    player.CharacterAdded:Connect(invis) --[ Waits until that player's character is added
end)

Please be sure to mark this as the answer if this worked for you :)

Have a great day! - DrShockz