Is it normal for a PhD student to be asked to contribute to a grant proposal? Is it common for a PhD student to be asked to contribute to a grant proposal (one of those that require faculty to submit them, the "big" ones)?

I've been asked to write a small section but I'm really worried that whatever I will write will be used to shoot down the proposal and that if that happens it will be my fault. I have no experience whatsoever writing grant proposals and have only minimal experience writing research (I'm a first year).

This is a big proposal for a multi-million dollar project. I don't want to be the reason for its failure.
You should have no cause for concern. If the grant is related to your work in any way then it is appropriate for you to be involved in the grant writing. 

But you aren't going to "shoot it down". In any reasonable case your work will be reviewed by others putting the grant together and also, especially for a large grant, a grants management office at the university. You might be asked to re-write your contribution once or twice with advice from those others.

It will be a good experience for you. If such large grants are an important part of your field, then you will want to learn what goes in to them so that you can lead it yourself later in your career. 

You might try to find writing samples from other grants to aid you. The research office or the PI can probably provide some older work. You can also try to work as closely as possible with others on the team. They likely have more experience than you do and can provide some guidance.