If you got to the Site Administration -> Developer -> Debugging section, you can enable the "Display debug messages" setting. Once that is enabled, it should disable the automatic redirect. If that is not enough, try setting the "debug messages" level to "DEVELOPER".
Of course this means that all users will see all the debugging messages everyplace on your Moodle.
In principal, alternatively, instead of setting "display debug messages" and "debug messages", you can set the variable $CFG->debugusers in config.php to a comma-separated list of user ids that should always see the messages. So if your user id is 99, put this in your config.php:
$CFG->debugusers = '99';
However, testing that on a Moodle 2.7, $CFG->debugusers doesn't work like that. The only way I could get it to stop before the page redirects was to enable "Display debug messages" and to set "debug messages" to "NORMAL" or higher.
A couple of other possibilities:
* Google Chrome includes a throttling feature. If you open up the developer tools panel in Chrome, you can change "No throttling" to GPRS. That should give you enough time to do a quick select-all / copy once the SMTP messages appear, and before the page redirects. You can then paste that someplace else and read it.
* You can use a tool like Wireshark to capture all the text that has been transmitted.