1000W (presumably with a bit more for any motor starting/inrush current) is on the higher end of such things for the average domestic transformer, especially if you want to try some kind of switch mode effort*. Worse is motors can be very picky about what input they take and it might well only work on a pure sine wave as opposed to the chopped up wave that some things use when they change voltages and I don't know what your mixer will be using.
I should also note that 60Hz is easier on electronics than 50Hz so things might overheat as well, and if it is a frequency driven motor then it might even be slower. If a proper client asked me tomorrow to make them a 60Hz supply from 50HZ input I could do it but you are never going to get it in a cheap device (RPC or VFD being the most likely candidates, though I could possibly cobble something together from a few UPS units).
*the simple answer here is get a building site transformer. Bonus being that with the switch to battery tools then such supplies can be had for next to nothing in the UK (don't know about the rest of Europe -- was watching a German guy the other day who repairs tools a lot and it seemed like he never encountered 120V stuff). But they usually have a honking great transformer in the middle of them and are quite heavy as a result (it is something you don't want to drop on your toes). For a switch mode supply then that makes life harder as that is getting up there towards the limit for most domestic type things and you start needing big boy stuff, and thus big boy prices.
I have seen a few isolation transformers around with 120V out for 240V in but I would say don't get one if you don't know what they are, especially not for a kitchen appliance.
At this point it might be easier to get a replacement motor if they do a European version (might be different size so check first) and see if that will do. However you might also face the other internals being used for it.