El alfiler perforó su dedo y se empezó a sangrar.

[system]

English Translation

The pin pierced his finger and it began to bleed.

Only common sense tells you it’s the finger and not the pin that started to bleed. I would suggest “El alfiler perforó su dedo, que se empezó a sangrar”.

[Adrianxu]

Well I wouldn’t use “se” at all. " El alfiler perforó su dedo que empezó a sangrar" or
“El alfiler perforó su dedo y empezó a sangrar”.