Hello. My SE is broken but haven't done a backup, if I take out the chip/SIM card will I loose all data (like voice recordings) from the SE if I put it in a new phone?

As Rudegar said, the SIM Card only contains your phone number. That means that the new phone will start receiving the calls and texts to the new phone, and your SE will not receive them anymore. Your SE will still hold all the old data, including your voice recordings. In what way is the phone broken?

If it is only external (cracked or likewise) you can still plug it in to a computer, and you can back up voice memories through iTunes (which also works on PC).

If it is internal, try and plug it in, and if it doesn't work, then I would suggest taking it to a certified apple repairer, or to a Genius Bar, and try to see what they can do.

All the best.