footcite does not show up in beamer

In your example the citation is showing up - but arguably in a very unhelpful format.

With most standard styles, the command footcite just typesets the normal citation label you'd get if you were to say cite in a footnote.

The example loads biblatex as usepackage{biblatex}, so requests style=numeric, which means you are using a numeric style where cite (usually) produces a simple number.

That explains what you are seeing here. footcite produces a footnote containing the citation label of the entry. The output is even more confusing since your version of beamer patches biblatex's bibliography output to replace the label numbers in the bibliography with cute little icons, so you have no way of knowing what each number refers to. (This is not the case in my version of biblatex and beamer, but I'm not sure if that is intentional or just a temporary thing.)

documentclass{beamer}
usetheme{CambridgeUS}
usepackage{biblatex}
bibliography{biblatex-examples}

begin{document}
begin{frame}{Deneme}
  begin{itemize}
    item lorem footcite{sigfridsson}
    item ipsum footcite{worman}
    item dolor footcite{sigfridsson}
    item sit footcite{nussbaum}
  end{itemize}
end{frame}

begin{frame}
printbibliography
end{frame}
end{document}

You might get a result that is closer to what you hoped for, if you use biblatex with the verbose style. Note that in that case there are no citation numbers at all, the only numbers you are seeing are the continuous footnote numbers.

documentclass{beamer}
usetheme{CambridgeUS}
usepackage[style=verbose]{biblatex}
bibliography{biblatex-examples}

begin{document}
begin{frame}{Deneme}
  begin{itemize}
    item lorem footcite{sigfridsson}
    item ipsum footcite{worman}
    item dolor footcite{sigfridsson}
    item sit footcite{nussbaum}
  end{itemize}
end{frame}

begin{frame}
printbibliography
end{frame}
end{document}

Often what people are hoping for are numeric citations with a sorted 'mini bibliography' of references cited on that slide at the bottom. That is much, much harder to achieve and I'm not aware of a good and robust solution for that at the moment. footcite - repeated references looked promising, but depending on the exact requirements you have in mind, a lot more may need to be done.