This is the bit that's outputting the heading:
printf( __( 'Category Archives: %s', 'slidingdoor' ), '<span>' . single_cat_title( '', false ) . '</span>' );
And this is the bit you don't want:
'Category Archives: %s'
The %s represents the category name. So if you want the category name to show, you'll need to change the code above to:
<span><?php single_cat_title( '', false ); ?></span>
That should work, I think. Although I'm pretty sure the span element is also redundant. I'd try it without and if all was well I'd leave it out, otherwise just put it back
You don't need all the printf() stuff and the __() stuff because you're not doing anything multilingual. You've deleted the only thing that could have been translated (i.e. 'Category Archives'), so you can just output the text directly.
If you don't even want the category name to show you can just delete the whole lot (that is, the whole lot in my first code block above).
If you're not doing this in a child theme, make sure you take a copy of the original code before you alter it so you can put it back if necessary.
If you do create a child theme, following the instructions I give in the link I posted, just copy your category.php file to your child theme and alter it there. If you make a mistake just recopy the original from the parent theme back over the file in the child.