The automation of key processes in metal cutting would substantially benefit many industries such as manufacturing and metal recycling. We present a vision-based control scheme for automated metal cutting with oxy-fuel torches, an established cutting medium in industry. The system consists of a robot equipped with a cutting torch and an eye-in-hand camera observing the scene behind a tinted visor. We develop a vision-based control algorithm to servo the torch's motion by visually observing its effects on the metal surface. As such, the vision system processes the metal surface's heat pool and computes its associated features, specifically pool convexity and intensity, which are then used for control. The operating conditions of the control problem are defined within which the stability is proven. In addition, metal cutting experiments are performed using a physical 1-DOF robot and oxy-fuel cutting equipment. Our results demonstrate the successful cutting of metal plates across three different plate thicknesses, relying purely on visual information without a priori knowledge of the thicknesses.