Jlevin, yes once the donation process completed system redirecting to same page with the message received from Authorize.net.
But you can redirect to any other page based on success/failure. For this you will need to make small change in one file. Here is the steps on how to do:
1. Go to plugin’s include directory. The path should be like ‘wp-content/plugins/wp-donate/includes’
2. Edit ‘donate-display.php’ file
3. Around line number 89 you will find a line of code like
header("Location:".site_url().$_SERVER['REQUEST_URI']);
4. You can add any custom page name here, for example
header("Location:".site_url().'/thankyou-page');
Note: you will need to create thankyou page before specifying it in URL.
Hope it will help.
https://www.ads-software.com/plugins/wp-donate