Remove numbers from CV bibliography using biblatex in Texshop

Add the following lines in your preamble

\DeclareFieldFormat{labelnumberwidth}{}
\setlength{\biblabelsep}{0pt}

The first line is to print nothing in the label, the second to eliminate the spacing before the entries.

MWE:

\begin{filecontents*}{cvreferences.bib}
@BOOK{book1,
  author    = {John Doe},
  title     = {Title},
  publisher = {Publisher},
  edition   = {edition},
  year      = {year},
}
\end{filecontents*}

\documentclass[11pt,a4paper,sans]{moderncv}
\moderncvstyle{casual}
\moderncvcolor{blue}

\usepackage[
   bibstyle=ieee,
   backend=biber
]{biblatex}
\addbibresource{cvreferences.bib}

\DeclareFieldFormat{labelnumberwidth}{}
\setlength{\biblabelsep}{0pt}

\firstname{John} % Your first name
\familyname{Doe} % Your last name

\begin{document}

\makecvtitle

\nocite{*}
\printbibliography[title=Publications]

\end{document} 

Output: