Like most materials, toffee (UK English) is elastic under low loads and plastic under greater loads. However, its response is highly dependent on both temperature (obviously?) and strain rate. If you load it quickly, it will fracture but, if you load it slowly, it will deform plastically. There's then a different stress-strain curve for each value of strain rate, which makes it difficult to analyse (although there are finite element studies of toffee in the literature). In practical terms, if you want to break a slab of toffee, hit it with a (toffee) hammer or bash it against your elbow.
More info: see Wikipedia Viscoplasticity.