Option 1
What you were trying to do (deleting the {block:HasTags} ... {/block:HasTags}
stuff) should actually have worked.. I recently had to add those to my own theme, since tags weren't being shown. Might be worth trying again, making sure not to change anything else? There might also be multiple places where that shows up and you'd need to delete them all.
Option 2
I don't think I'd recommend @Gabrielle Martin's answer the way it currently looks, since it could also hide where you reblogged something from. If you were going to try it, though, find the first place you see either <style>
or <style type="text/css">
and add what she suggested right after that.
Option 3
Another thing you could try would be adding a bit of inline CSS. Anywhere you see this:
{block:Tags}
<li>
You want to change it to this:
{block:Tags}
<li style="display:none;">
Ignore the </li>
s, they're fine as-is.