"A cada cerdo le llega su San Martín" means that every person, no matter how powerful and important could he be, will reach, unavoidably, his moment of failure and disgrace. I'm not sure that this could have an equivalent proverb in English, at least, I didn't find it. The San Martin day is when, in the Spain countryside, they butcher the pigs for making ham, sausages. etc. For most of the poor pigs is the final day of their lives.
"De tal palo tal astilla" is equal to "like father, like son.