Step down transformer for a 1 HP Kitchenaid mixer
There are two types of transformer (amongst the other types).

You can buy an isolating transformer, the sort that's used for most applications. As the name suggests, these have a mains winding, and a secondary winding, with no electrical connection between the two.

Or you can buy a non-isolating auto transformer. This shares a winding between input and output. While a no-no for applications needing isolation, powering appliances that are designed to be direct connected to the mains is just fine. Because it shares a winding, it's about 50% lighter and smaller (but I doubt as much as 50% cheaper) than an equivalently rated isolating transformer.

What size to get?

If you assume that 350watt rating is the output power of the motor, then it sounds quite reasonable that 1HP (~750 watts) could be the input power. 

So 750 watts is a safe size to go for.

However, transformers can be overloaded for a while, and if turned off before they get too hot, that's OK. Does the mixer draw full power all the time, or only when making ground beef? Take those two together, and you may get away with a lower rated transformer that you use intermittently, and keep an eye on the temperature.