If someone is penny-pinching, they really do not like to spend or give money, even in small amounts. They hold on to every penny. It is not a kind word: it suggests the person is too tight, not merely careful. You can call a person penny-pinching, or talk about penny-pinching habits, or penny-pinching cuts when a government or company trims every small cost. The older word behind it is pinchpenny — the two halves later swapped places. The phrase is informal and a little sharp; in polite talk you might say careful with money instead. It is about money, not about literally squeezing a coin, though that picture is how the saying was born.