Como dizer "Dar o sangue" em inglês

Uma sugestão:

Do everything for somebody

I do everything for my family and I want to support them as long as I can.

To give (someone) the shirt off one's back.
To give anything or everything you have; to be extremely generous and helpful; to be willing to sacrifice to help others
Exemplo: I give my family the shirt off my back. (Eu dou o sangue pela minha família)

And could also be:
I work to the bone, I care, I support my family and I am always there for them, everyone of my family.

Another way would be "I give my all for my family" as in:
"I am a family man. I give my all for my family.

"I give my all for my family, and nothing less will be tolerated. We fight together to win as a family, we play the game as a family, and we win as a family."

I go the extra mile for my family.

Ana yet another way: "I gave my all for my family."

In sports, players usully say "I gave my all for the club..." and "I gave my all to the game...".

"Do one's best"/show commitment/work hard.

Vamos dar o sangue, jogar com raça vamos ganhar e levantar o caneco.
Let's do our best, play with grit, let's win and raise the trophy!
(Soccer pep talk, after having conceded 6 goals and scored none in the first half of the match)

Português: dar o sangue, dar o máximo de si, esforçar-se ao máximo, fazer o máximo que puder.
Inglês: to strain every nerve, to go the extra mile.

Exemplo 1: Greenpeace strained every nerve, tried every tactic and mobilised every resource to give our colleagues a fighting chance. Ref. greenpeace.org

Exemplo 2: Sally added: “Our crews and call handlers always go that extra mile, now it’s your chance to go the extra mile for them!” Ref. londonambulance.nhs

Cf. Como dizer "Tudo ou nada / oito ou oitenta" em inglês