As a general rule, folks don't like you to self-promote your own pages on sites like StumbleUpon. I have submitted my own posts in the past – but rarely. If I thought the post was controversial or could gain a lot of attention for its impact, I might Stumble it myself. Otherwise, I just hope that others will like the page and give it a thumbs up.
That said, there's nothing wrong with going back and giving a thumbs up for pages that others have already Stumbled Upon within your website. If you try searching for your domain or website within StumbleUpon, you'll find their search is pretty pitiful and limited to the tags that users fill in.
Side note: If I were StumbleUpon, I would totally implement Google Custom Search as a revenue source.
Using Google, though, you can easily find which of your site's pages have been Stumbled so you can throw an extra vote in! For my blog, I just search for:
This provides me with a list of my pages that others have Stumbled so that I can tack on another vote. Self-serving? Perhaps – but I lean in the direction that its okay because someone else has already deemed the post worthy of Stumbling.
If you're on StumbleUpon, be sure to add me as a friend.