(1) I bought a knife to cut bread with.
I think possible interpretations of (1) would be:
a) I bought a knife with which I/you/one can cut bread. (This implies that not all knives are appropriate for cutting bread; I bought one with which it's possible to cut bread)
b) I bought a knife with which I intend to cut bread. (This is talking more about my intentions than the type of knife)
(2) I bought a knife to cut bread. (This means I bought the knife in order to cut bread; purpose, intentions)
Q: What would be the difference in meaning between sentence (1) with interpretation (b) and sentence (2), which both only suggest my intention to cut bread? In other words, if it's interpretation (b), can I say that the preposition "with" is optional in sentence (1)?