How do you take off your avatar on Xbox 360 profile?

You can't. A randomly generated avatar is given to you. You can change it in the avatar editor, if you do not like it.

Your avatar items are all there on XB1 but there is no real avatar support as in say your friends list like on the 360. You can take snapshots of your avatar for gamerpics but that's about it really. But yes you do have access to everything.

Hello DrLix,

We take our avatar information from the Xbox 360. If you would like to change the avatar shown on the Rewards website, you will have to adjust it from your Xbox 360.

You cant delete avatars, but you can change them. Go to the Xbox 360 dashboard, select the Sub-Title "friends" and click on your avatar. This will take you to "Avatar Editing". From there, you can edit, and personalize your Xbox 360 Avatar I hope I helped
Have a good day

You need to take a picture of your Xbox avatar within the avatar editor. To do this, you can just click on your name here in the forums. That will take you to your Xbox.com account page. Choose Edit My Avatar and then Gamer Picture from the menu within the
avatar editor. You can choose a background color and make your avatar do expressions. Click on Take a Picture. You can take up to three pictures. Select the one you like and choose save. It can take a day for the new avatar picture to appear next to your gamertag
but it will appear! =)