How to get rid of the "Oxford comma" in a listing of three or more authors?

Use

\DefineBibliographyExtras{english}{%
  \let\finalandcomma\empty
  \let\finalandsemicolon\empty
}

to get rid of Oxford commas (and semicolons) in general. Since the definitions live in the .lbx files you can't simply change them in your preamble, you need a language-specific \DefineBibliographyExtras. Many other languages including british don't use the Oxford comma by default, so you could consider switching if you don't write in American English.

\documentclass[a4paper,10pt]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[english]{babel}
\usepackage{csquotes}
\usepackage[style=alphabetic,maxnames=10]{biblatex}
\addbibresource{biblatex-examples.bib}

\DefineBibliographyExtras{english}{%
  \let\finalandcomma\empty
  \let\finalandsemicolon\empty
}

\begin{document}
\nocite{companion}
\printbibliography
\end{document}

To remove it change the definition of \finalnamedelim.

\documentclass[a4paper,10pt]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[english]{babel}
\usepackage{csquotes}
\usepackage[style=alphabetic,maxnames=10]{biblatex}
\addbibresource{references.bib}
\usepackage{filecontents}
\begin{filecontents}{references.bib}
@book{key,
  author = {Baur, S. and Schmid, A. and Schur, B.},
  year = {2001},
  title = {Title},
  publisher = {Publisher},
}
\end{filecontents}
\DeclareDelimFormat{finalnamedelim}{\addspace\bibstring{and}\space}

\begin{document}
\nocite{*}
\printbibliography[heading=bibintoc]
\end{document}