How can I block and delete a contact from mixi (MIXI.JP) .?

I'm not quite sure what you mean by "contact from mixi" though...

If you have your mixi and don't wanna get コミュニティ・ニュース(community news) and/or notification of getting messages:

-Click 設定変更 at the very right of the top tool bar

-Click 基本設定 at the right of the three choices appear

-Type your password and click 次へ進む

-Check 受け取らない in the メッセージ受信通知メール and/or コミュニティ・ニュース

-Click 入力内容を確認する

-Click 変更する

Then if you just don't wanna anything from mixi.jp, quit mixi and block it as you do for junk mails.

Hope this helps.

Click 設定変更, その他の設定.

Then enter ID of the person you want to block in アクセスブロック boxes.

And you can block the person.