How to replace a string in a URL field when outputting it in a template file
You probably want a preprocess function in your template.php for this. In your case, hook_preprocess_field() will be easiest to work with - for an example of how this is implemented, check out the API documentation for template_preprocess_field(). 

Remember, $variables is passed into preprocess hooks by reference. From within your hook_preprocess_field(), instead of modifying the field data directly (in case you need it elsewhere), you could do something like this after checking that you're operating on the right field:

/* devel's dpr() is handy for seeing where in the $variables array it lives if you 
   don't have a debugger handy. If you see 'und', that's the value for the LANGUAGE_NONE
   constant. It's considered best practice to use the constant instead. */
$slave_link = $variables['field_url'][LANGUAGE_NONE][0]['value'];  
$slave_link = str_replace("http://", '', $slave_link); // Trim http://
$slave_link = str_replace("master", "slave", $slave_link); // s/master/slave
$variables['slave_link'] = $slave_link;  /* You can now access this variable from your
                                            field--field_url.tpl.php as $slave_link */


You may also need to clear your cache after making these changes.