Note: the answer below is valid for Biblatex/Biber as contained in TeX Live 2014 (and maybe some earlier versions as well). Starting with TeX Live 2015 a refsection is treated as a fully independent environment with a counter starting at 1, which is not influenced by resetnumbers=false. However, it does respect resetnumbers=n. Therefore, you can store the last number of a refsection and set the number in a new refsection to the stored number + 1.
Full credits go to @moewe for providing an implementation of this solution on https://github.com/plk/biblatex/issues/1222.
Code (cf. full MWE in original answer below):
\begin{document}
\begin{refsection}
Some text \autocite{B02,A01}.
\printbibliography[title={References1}]
\numgdef\resetnum{\csuse{blx@labelnumber@\therefsection}+1}
\end{refsection}
\begin{refsection}
Some more text \autocite{Z00,C03}
\printbibliography[title={References2}, resetnumbers=\resetnum]
\end{refsection}
\end{document}
Original answer, valid for TeX Live 2014:
This can be done using refsections, each containing a bibliography for the citations used in that refsection. The global option sorting=none for BibLaTeX results in references numbered in the order they appear in the text. The option resetnumbers=false for a printbibliography combined with the global option defernumbers=true results in continous numbering across refsections. You may need to delete the .aux, .bbl, .bcf, .blg files at some point if the result is not as expected.
MWE, adapted from https://tex.stackexchange.com/a/42273/89417:
\documentclass{article}
\usepackage[sorting=none,defernumbers=true]{biblatex}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@misc{A01,
author = {Author, A.},
year = {2001},
title = {Alpha},
}
@misc{B02,
author = {Buthor, B.},
year = {2002},
title = {Bravo},
}
@misc{C03,
keywords = {pub},
author = {Cuthor, C.},
year = {2003},
title = {Charlie},
}
@misc{Z00,
keywords = {pub},
author = {Zuthor, Z.},
year = {2000},
title = {Zulu},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
\begin{refsection}
Some text \autocite{B02,A01}.
\printbibliography[title={References1},resetnumbers=true]
\end{refsection}
\begin{refsection}
Some more text \autocite{Z00,C03}
\printbibliography[title={References2},resetnumbers=false]
\end{refsection}
\end{document}
Result:
