Currently there is no way to download the data used to populate the “Audit Logs” panel, some people have suggested to add a button to be able to export this data but I am still unsure of how to do this without open a security hole in the code. However you can extract this data without paginate through every page in that panel, but this requires manual data mining.
I simplified the commands that you must use to retrieve all the logs from the remote Sucuri server in this script [1], if you know how to use Curl [2] then you can configure this script with your API key and the number of logs that you want to retrieve. If you know how to use HTTPie [3] then it will be easier because the response is in JSON and this tool automatically formats that output in a human readable way.
If you do not know what Curl and/or HTTPie is then I ask you to be patient while I implement the code in the plugin to allow the exportation of the audit logs because this will take some time.
[1] https://cixtor.com/pastio/uo8j6t
[2] https://en.wikipedia.org/wiki/CURL
[3] https://httpie.org/