What would be the best way to report someone for sending me death threats?

Block communications and report the player via the console tools is all you can do.

If you feel the death threats were genuine report them to your local police authority

Cops.  Police. The Fuzz.  Whatever you kids call them these days (goes on about his business with his walker)

I recommend the police.

I've been having problems with this person online in the SCV new york lobby. she has sent me rude mean messages and spread slanderous rumors about me i muted and blocked her on both of her GTs. She found my FB two weeks ago and bashed my photos and made me cry my eyes out and had her friends harass me. Now i learned last night shes sending my pictures around to random ppl on xbox. i want her to stop after i muted her i never had to deal with her again. and i had made my FB private that night but she saved my pictures. i have job interviews lined up. im scared shell ruin me and put a fake account on something horrible with my name and a picture. i called microsoft and the said right a post here so i could get help cause they cant ban her themselves. please help i don't know what to do. im tired of being picked on here. i came here to have fun and game not be treated like I'm in high school. shes sending them via kinect. i only found out when my friend told me and sent me the message she got. and its me its my face in my kitchen. muting her and blocking her wasnt enough whats the next i need to take. 

You may want to post a new thread or follow the same instructions.... REPORT--- AVOID and BLOCK.  GOOD LUCK

T.T

LOL "REPORT AVOID and BLOCK" In my opinion  If you don't BLOCK COM then you may have more proof of threaten you, AVOID its not posible if you are from the same area, you will be matched witch the same server eg. when i mark someone as avoid player i still play with them every day, REPORT i did on person who is using illegal copies of the games, he is downloading the games for free and doing this for ages and still is online. So you can try Report and definitely dont BLOCK!! The best thing to do is to go to the police and tell them the story and show all the messages and say that you are afraid now and they definitely will tell you what to do. Good Luck

just block him, lol.  Don't call the cops.  The guy isn't going to try to find out who you are and your address.  That's silly.  

Contact your ISP provider, inform them of the event.  Contact your local law enforcement and have them take your statement so they can open up a terroristic threatening case.  They will exchange the information with law enforcement and if the claims are valid and the person did indeed make these threats even if it was a joke they can be facing some serious jail time.