Okay. I used the array_shift function to remove the resource id from the front of the array. I don't know if this is the most elegant way to go about it, but it seems to work so I can live with it!
Here's the final version of what I'm using:
$query_records = "SELECT * FROM category";
$records = mysql_query($query_records, $db) or die(mysql_error());
$records_array = mysql_fetch_assoc/B;
$remove_catid = array_shift/B;
$final_array = implode(',', $records_array);
print_r($final_array);