Mach 3 is a very good program. However it may not be the best choice for this kind of simple task. You will be running windows on a PC. Do you have any 15 year old PCs that have never been powered down except in a power failure? I have several PLCs that have been running continuously for 18 years! Because that is what PLCs are made to do.
So an Automation Direct DL06 as an example, with a high speed counter module and a micro graphics terminal will cost you about $700 and you can drive a stepper, a servo, a 1 HP DC motor using a $150 controller, or a 3 phase motor from a $150 VFD for this little project. You'd have 20 inputs and 16 outputs for safety switches, limits, selector switches, etc. Ladder logic programming gives you if/then/else timers, counters and on an on. You do want to count how many pieces of each length you cut right?
In fact my multi-purpose CNC has one in it, along with Mach 3. I have a selector switch for the high speed router spindle or the high torque R8 spindle. There is another one for Mill/Lathe/3d printer, another for air blow off/none/coolant, and one for Spindle On/Off/Auto with Mach 3. There are door switches and limit switches on the axis that kill all power, and key switch to override the door switches. There are two conveniently located pushbuttons programmed as toggles for the vacuum cleaner. Mach 3 also has inputs to the PLC. I drive the vacuum outlet, two spindles, a heated bed, a nozzle heater, and Mach 3 handles 4 axis motion.