You have to pass a function to expect. Like this:
expect(model.get.bind(model, 'z')).to.throw('Property does not exist in model schema.');
expect(model.get.bind(model, 'z')).to.throw(new Error('Property does not exist in model schema.'));
The way you are doing it, you are passing to expect the result of calling model.get('z'). But to test whether something is thrown, you have to pass a function to expect, which expect will call itself. The bind method used above creates a new function which when called will call model.get with this set to the value of model and the first argument set to 'z'.
A good explanation of bind can be found here.