You can if what you need is 240 single phase. Such a transformer may have a European-style outlet on it, though, with one pin grounded and the other at 240. If so you will want to rewire it. There probably won't be a center tap so you will have to either leave the secondary floating or run it European-style.
You could also rig an autotransformer from a 1:1 120V transformer, but if you knew how to do that you'd find it easier to just put in a subpanel.
Much better to just put in a subpanel.
If the mill is wired for only 240VAC - i.e. its power cord only has three conductors (two hots and the ground), then the transformer should work fine. The mill doesn't care if one leg of the 240VAC is at ground potential and the other leg is at 240VAC potential, or if both legs are at 120VAC potential reference to ground but 180 degrees out of phase. The mill only cares if the difference between the two legs (the two current carrying conductors) is 240VAC.
If the mill also has a 120VAC load, such as for any lights or controls, then such a simple transformer won't work because it isn't designed to provide both 120VAC and 240VAC loads measured between the current carrying conductors (the hots and the neutral). If the mill also has a 120VAC load then its power cord will have four conductors.
The challenge I see with this transformer is changing the provided Euro/Asian Shucko round plug to a plug useful here in the U.S. Maybe the free adapter plug that comes with it does this change. Also, I don't know if the motor in-rush current will cause any issues when the mill is started.
Look at the breaker feeding the garage receptacle that you want to use with the transformer. If the breaker is 15A then you can drive a 1/2HP or smaller, 240VAC motor by the circuit according to code (assuming nothing else is on the circuit). If the breaker is 20A then you can only drive a 1HP or smaller, 240VAC motor by the circuit according to code. This assumes that the transformer does not have any loss, which it will have some.
I say "according to code", for the NEC builds in safety factors when sizing the conductors and breakers. The circuit breaker is only there to protect the circuit conductor, and not anything that is attached to the outlet. Also, when sizing the circuit conductors for a motor-driven appliance, the full load current is determined from an NEC table and not from the current nameplate rating. All the motorized equipment I have around my house have nameplate full load current ratings smaller than what NEC specifies the circuit can to handle. Finally, circuit breakers have a time/current curve such that they don't immediately trip when the current slightly exceeds their rating. How long it takes a breaker to trip is inversely proportional to the amount of the overcurrent.
So yea, it may be possible to drive a motor larger than what is specified by code by doing things such as minimizing loading down the motor or limiting how often it is started up, or just not continuously running the motor for long periods of time. But none of these things would be recommended by anyone (including myself) who could be in a position to be considered liable if a fire were to start. But there is nothing preventing a homeowner from making due with the wiring that he currently has until he can get a better solution - there is nothing preventing someone from plugging in equipment that pulls a little more power than what the circuit was designed for.