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.