My grandma forgot her iPhone password and we're trying to get here data off?

Is there any hope that we might be able to get her data off her phone. Just though of removing the SIM card would that work?

Not at all.
The phone has to be reset to factory specs, which will wipe it clean.
Only a Recovery, or (police type) forensics lab might be able to recover the data. Very Expensive if it can be done.

Hmm, sounds fishy.

She should go to her email account and reset the password

It is not possible. Your only hope is if she had icloud back ups or iTunes backups on a computer. You will be able to erase the phone to get it back to a usable stae by using recovery mode, but you won't have any of the data with out those back ups. BTW, removing the sim card wouldn't do a thing except give you no service on the phone.