Ending an executed function in a different function?

Stop the loop from somewhere else.

local condition=true
function Loop()
    while condition do
        wait()
        print("loop")
    end
end

function OtherFunction()
    condition=false
end

In the case of a loopkill program, it would actually be best to connect to CharacterAdded instead of repeatedly and redundantly killing the dead character.

Based on what you posted

local loopkill={}
function onChatted38(message,player)
    if message=="loopkill" and Admin[player.Name] then
        loopkill[player.Name]=true
        while loopkill[player.Name]do
            wait()
            player.Character:BreakJoints()
        end
    elseif message=="unloopkill"and Admin[player.Name]then
        loopkill[player.Name]=nil
    end
end

Using CharacterAdded

local loopkill={}
function onChatted38(message,player)
    if Admin[player.Name]then
        if message=="loopkill"then
            loopkill[player.Name]=player.CharacterAdded:connect(function(character)
                character:BreakJoints()
            end)
            player.Character:BreakJoints()
        elseif message=="unloopkill"and loopkill[player.Name]then
            loopkill[player.Name]:disconnect()
        end
    end
end