User Problem

Currently, Trello doesn't have the ability to download/export other members activity.

Suggested Solutions

It would be great to have an export action, similar to the ones we have for the cards and board.

Current Workarounds

You can view the activity of a specific user by going to their profile. You can access a user's profile through the link https://trello.com/u/<username>/, or by clicking their profile picture icon in a board's member list. It won't be possible to download the file, but the information is available through the user interface.

Note that their activity tab will only show actions performed on boards/Workspaces that you have in common.