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"
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Select any portion of the document and tap "Paste" to make sure the clipboard contains only non-printing characters.