If you do not wish to save the file to Document Cloud, you can simply save it on the device.
The PDFs that you open in the Adobe Acrobat Reader do not get saved automatically to document cloud.
If you are using the application on the mobile device, you can use it without signing in to the application.
There is no direct option to turn off the Document Cloud from the application.
Hope that answers your question.
Let us know if you need any help.