The whole purpose of Mello kidnapping Kiyomi Takada was to either: A. Get information from her as to the identity of Kira (before Near). -and/or- B. Use her to get to the Death Note which Mello thought she had access to. As for Matt's motivation, it is thought that he was trying to help/impress Mello and further ingratiate himself to his cause in beating Near to Kira.