The iPhone clipboard -- or in Apple terms, "Pasteboard" -- holds only one item at a time and has no native function that clears it. If you want to clear the clipboard, for security reasons for example, you can achieve a similar effect by copying a non-printing character, like a hard return or a space, so those invisible characters replace Pasteboard's contents.
Open any app or area in your iPhone where text can be entered. Tap "Return" a couple times and perhaps the Space Bar a few times for good measure. This creates a section of the active document with non-printing characters that can be copied, deleted and pasted, just like any other text.
Highlight the space you created with hard returns and the space bar. Select "Copy"
Select any portion of the document and tap "Paste" to make sure the clipboard contains only non-printing characters.
If you want to truly clear Pasteboard, there are options in the App store that can help with this task.
NoteBox: Notebox has a "Today Widget" that shows the items on Pasteboard and allows you to clear them at any time.This productivity app allows for collecting clips and sharing between devices and to sites like Evernote and Dropbox and also to social networks.
1Password: Set the "Copy to Clipboard" setting to "On" and under "Security," set the amount of time before the clipboard is cleared. Though this doesn't clear the clipboard whenever you want, but it does clear out the information you may be most worried about. 1Password stores sensitive information like credit card numbers, driver's license and website logins and makes them accessible with one master password.
IClear My Clipboard: This is a uni-tasking app -- its sole purpose is clearing the clipboard. Strangely, it has a big red delete button for clearing the item you are viewing in iClear, and an option in the top right of the screen for "Clear All." Since Pasteboard holds only one item at a time, one might ask why it needs both.
- Apple.com: IPhone User Guide
- GetNotebox.com: IOS Clipboard -- Productivity vs. Security
- Agile Blog: 1Password for iOS Features: There and Back Again With Clipboard
- Agilebits.com: 1Password for iPhone and iPad
- ITunes Preview: NoteBox -- Collect, Organize and Share Text
- ITunes Preview: IClear My Clipboard