Single phase induction motors are designed to run at full voltage and constant speed. Causing the speed to reduce by any means. changing voltage, running on part cycles or reducing the frequency will all cause the starter winding to kick back in (usually with a centrifugal switch) which will cause problems.
For a hacksaw, the best option is to seek out a 6 pole motor which will run around 950 rpm and reduce the speed with a belt drive. A four pole (1425rpm in uk) will be Ok with a smaller motor pulley but the 2 pole (2850 in Uk) will be just too fast for the application.
The very successful Kennedy saws use a flat belt drive giving good grip on a small diameter crowned motor pulley and a flywheel around 6-9" according to model to drive the crank. Modern source for flat belt drive is to use a toothed belt running on its back. My kennedy model 90 has been running like that for several years perfectly.