If there are no Automatic Store operations configured for the SD Card, such as the option to automatically transfer the Event Log from the controller's memory to the card at 80% full, or highly cyclical SSV Messaging to transfer it, then you should be able to remove the SD Card at any time while the controller is in Run Mode.
You could have a controller logging away to its internal buffer and then use a HMI button to execute a manual Store operation to the SD Card. Then remove it for your perusal.
Personally, if the logged events were required to be readily available, I would be more inclined to GSV them into tags and create a log page on a HMI or SCADA to display them.
I do not think that a manual Store operation to one SD Card will execute a similar operation for the redundant controller. But if it was done programmatically, and both controller's project were synchronised, then an automatic Store operation would indirectly execute in tandem, once both controllers are in Run Mode.
Regards,
George