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Although it should be safe, I would advise you NOT to run power tools from a transformer modified as shown below. Site transformers were originally designed for running power tools and the earthing arrangement was presumably designed to suit this application. This modification should ONLY be done if you are comfortable working with mains voltages and know your wiring code.
Scary words aside, why would you want to do this? Well, I use it to provide a source of totally isolated 110VAC which, for example, I can rectify and smooth to give me a 170VDC supply for powering things like induction heaters or ultrasonic transducers. Point being that, since the 110VAC source is totally isolated from the mains, it means it's possible to then earth the negative rail of the rectified DC supply, making it safer to work with.
Site transformers normally have a center-tapped secondary, with each half of the secondary providing about 55VAC each, giving 110VAC across the total. The center tap is connected to the transformer core, which is normally grounded. This means that the greatest voltage a user would ever be exposed to is only 55VAC relative to earth, making it much safer. The modification is simply to remove the earth connection to the transformer core, so the entire secondary is now floating, and either end may be grounded (or used to run an external circuit, part of which is grounded). Make sure, however, that you maintain an earth connection from the mains input to the earth pins on the output sockets.
Click here for the schematics. The top diagram shows the transformer before, and the bottom shows it after. This is a typical small 2-output transformer - circuits may vary for other types/sizes. The pictures below show the modification. Look at the top-left wire in the terminal block in the second picture - this goes to the transformer core, and is now disconnected. However, earth continuity is maintained between the mains input and the output earth pins.
 Before |
 After |
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