I was actually just looking into this last week.
There used to be a vendor out of Chicago(?) that made original spec replacement parts for hamilton beach appliances - I bought a new set of beaters for my mom's old mixer about 10 years ago after my dad jammed them with a wooden spoon - but they closed up shop just a few years later.
There is also a section on the hamilton beach website where you enter the model or serial number of the machine and it gives you a list of replacement parts available.
Ebay, amazon, and surprisingly enough Etsy, seemed to be the most popular places for these things to change hands.
Not sure if this fits your particular model:
Mixer cup, fits Hamilton Beach 936, 950 Drink Mixers | eBay