If you want a separate tree you have full control over then Geni is probably not the site for you, and probably not any online programs either. Only a standalone program on your personal computer can give you that. You could however give the owner company, MyHeritage a try.
I notice that you are part of the world tree, and there is as many as 13 Geni users within your own family group, so your tree cannot be automatically deleted if you close your account because it would ruin their tree as well.
http://www.geni.com/worldfamilytree/learn-more
You find the option to close your account in the account settings you find in the menu that pops up when clicking your own name in the upper right corner. When closing the account you will get some options on what to do with your profiles, bus as I said above probably only your own profile can be deleted. If you were is a standalone tree as the only user the whole tree would be deleted.
Since you are currently connected to the World Tree, closing your account would not delete any Profiles - and I believe it would be considered against the Terms of Service to delete any of them (again, because they are part of the World Tree).
Are you sure you want to be start over and try to create this stand-alone Tree on Geni, rather than on MyHeritage or some other site? Geni is truly trying to focus on the creation of a World Tree. Could you perhaps ask a Curator to help you untangle whatever mess leads you to feel you need to start over?
If you decide you definitely want a new stand-alone Tree, and want it on Geni, my suggestion would be - use a different e-mail, and do not close the current account -- that way, you can still get in to the old account if you ever decide you want to - either to undo errors others are making, or whatever.
In addition to the very good comments above, I was wondering if you're overwhelmed by your view of your tree. You can adjust your tree settings to no more than, say, three generations at a time. That should keep you focused on your own entries and not overwhelmed by what more distant cousins have contributed you cannot verify quality on.
And to repeat - if there's a mistake it can be fixed, we have a "curators please assist" discussion for that; links to the Geni profiles in question posted, please.
I hope this helps.