Simple:Press is displayed using templates so to remove, change, add items it is just a matter of making edits to the relevant template.
In this case the template you need is spHead.php which is in the /templates folder of the SP theme you are using.
You will want to comment out or remove the following display template functions:
sp_LogInOutButton()
sp_RegisterButton()
sp_LoginForm()
and that should give you what you need.
As always we recommend that you create your own SP theme so that any customisation is not lost during a future update. (http://codex.simple-press.com/codex/themes/theme-basics/creating-a-theme/)