Coin clipping was already an established (though illegal, and heavily punished) process. Coins were made from precious metals, and the edge of the coin could be clipped off, melted down and sold. This could be achieved with a strong pair of shears and/or a file. The Royal Mint has a fun little run-down of coin defacement crimes intended for teachers, and it mentions tools and processes used to break coins. (opens a pdf)

While Loreen L. Giese talks about the exchange of halves of a broken coin in her book Courtships, Marriage Customs, and Shakespeare's Comedies, there is also evidence that the coin was not necessarily broken, but could also just be bent. Giese mentions this a little, but David Cressy discusses it in a little more detail in his book Birth, Marriage, and Death : Ritual, Religion, and the Life-Cycle in Tudor and Stuart England. He mentions cases where the coin is sometimes whole, as well as only bent, and can still be treated as an offer of marriage (or contested as such at any rate!). The link I've given there should take you straight to a description of such tokens. Bending the coin could of course be achieved with as simple a tool as a hammer.