Why won't my weapon tag the player?

The reason you're getting this error is because you define the functions tagHumanoid and untagHumanoid after the loop; so, while the loop is running, those functions do not exist. This can be easily remedied:

wait(0.01)
local CanDamage = true
local plr = game.Players.LocalPlayer

local function tagHumanoid(humanoid, player) --// Usage of local functions is recommended
    local creator_tag = Instance.new("ObjectValue")
    creator_tag.Value = player
    creator_tag.Name = "creator"
    creator_tag.Parent = humanoid
end

local function untagHumanoid(humanoid)
    if humanoid ~= nil then
        local tag = humanoid:FindFirstChild("creator")
        if tag ~= nil then
            tag.Parent = nil
        end
    end
end

while true do
	wait(0.01)
	script.Parent.Touched:connect(function(hum) -- Changed "part" to "hum"
		-- local hum = part.Parent:FindFirstChild("Humanoid") Delete this
		if hum and hum.Parent:FindFirstChild("Humanoid") then -- "hum" is the Player who touched the part/Sword.
			if CanDamage == true then
				tagHumanoid(hum, plr)
				CanDamage = false
				hum.Parent.Humanoid:TakeDamage(10) -- I forgot to add the "Parent.Humanoid" part after "hum"
				plr.swordlvl.Value = plr.swordlvl.Value + 2
				wait(0.8)
				untagHumanoid(hum)
				CanDamage = true
			end
		end
	end)
end

Hope this helped!

PS: Your indentation was a bit off, so I went ahead and fixed it for you. In the future, it's a good idea to always properly indent your code so it's easier to read.