Did you see the beautiful deck of playing cards drawn by Antonio Vargas, depicting the conquistadors as well as the four big historical tribes of Mexico (Maya, Olmec, Toltec, and Aztec)? He explains to us that, although very scholarly, the Mayans were no slouches on the battlefield:
 

Y también se ponían sus buenos catorrazos,

And they also gave good blows,

pero eran un pueblo de mucho conocimiento...

but they were a people of much knowledge...

Captions 39-40, Antonio Vargas - Artista - ilustración

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Have a look at one of our previous lessons,  —azo: a painful suffix, and you will learn that the suffix "-azo" gives the meaning "a blow/hit from." For example un palazo is a hit with a stick (palo) or a shovel (pala), and a tortazo is what you receive when you get in the way of a moving torta (cake)!

So what about these catorrazos that Antonio refers to, and that we translated simply as "blows"? Sources tell us that the root word is cate, a rather obscure Spanish word synonymous with golpe, and which itself means "hit" or "blow,"—which would give us a "blow" by way of a "hit" (or a hit by way of a blow). Obviously a bit redundant!

Catorrazo is very colloquial, and is primarily heard in Mexico. In actuality, bilingual dictionaries define it as simply a "punch," a "blow," or even "a hit with a stick or billy club."
 

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Here's an interesting tidbit: Since the word for "fist" is puño, we might be tempted to also try puñazo for "punch." However, the word you are most likely to hear (and what you will find in the dictionary) is slightly different, "puñetazo." However, puñazo is also seen occasionally, and, in Latin America, the word puño itself doubles for "punch" as well.