Why doesn't this script work? Its supposed to teleport you behind a target

By using CFrame.new(0,0,3), you are adding 3 to the CFrame on the z-axis. In this instance, you will only teleport behind the enemy if they are parallel to the z-axis. What you should try instead, is use the lookvector of the enemy and teleport behind them that way. A CFrame's lookvector is a directional vector with a magnitude of 1 that tells you where the front-surface of a part is facing.

function module.DistanceFromKill()
        local nearestEnemy = nil
        local nearestRoot = math.huge 
        workspace.SmilingKidWithRope.SmilingKid.Parent = workspace
        local root = workspace.SmilingKid.HumanoidRootPart
        for i, v in pairs(workspace.Game.People:GetChildren()) do 
            local plrRoot = v:FindFirstChild("HumanoidRootPart")

            if plrRoot and plrRoot ~= root then
                local mag = (plrRoot.Position - root.Position).Magnitude
                if mag < 10 and mag < nearestRoot then
                    nearestEnemy = plrRoot
                    nearestRoot = mag
                end
            end
        end
    if nearestEnemy then
    local newpos = nearestEnemy.Position
    local lookvector = nearestEnemy.CFrame.lookVector
        root.CFrame = CFrame.new(newpos - lookvector * 3, newpos + lookvector)
        end 
end

This will teleport them behind the enemy as well as have them face where the enemy is facing.