Bibliography per chapter with continuous numbering

Use of refsegment will continue label numbering for you. To print a reference in just one sub-bibliography (and completely frustrate most readers), you can track the continuation number for each refsegment and skip any items whose label is less than that number.

In the example below the default sorting scheme is used, but it could be changed. To get the label numbers right, this approach will require a couple additional passes with latex. biblatex gives you a message whenever another pass is needed.

\documentclass{report}
\usepackage[sorting=none,style=numeric,refsegment=chapter,defernumbers=true]{biblatex}
\usepackage{filecontents}

\defbibheading{subbibliography}{%
  \section*{Bibliography}}

\makeatletter

% Overall entry counter
\csnumgdef{blx@entrycount}{0}
\AtEveryBibitem{%
  \csnumgdef{blx@entrycount}{\csuse{blx@entrycount}+1}}

% Continued from this label number
\appto{\newrefsegment}{%
  \csnumgdef{blx@entrycount@\the\c@refsegment}{\csuse{blx@entrycount}+1}}

% Skip entries with label numbers less than the continued number
\defbibcheck{onlynew}{%
  \ifnumless{\thefield{labelnumber}}{\csuse{blx@entrycount@\the\c@refsegment}}
    {\skipentry}
    {}}

\makeatother

\begin{filecontents}{\jobname.bib}
@Book{companion,
  author = {Goossens, Michel and Mittelbach, Frank and Samarin, Alexander},
  title = {The LaTeX Companion},
  edition = {1},
  publisher = {Addison-Wesley},
  location = {Reading, Mass.},
  date = {1994}}
@Article{gillies,
  author = {Gillies, Alexander},
  title = {Herder and the Preparation of Goethe's Idea of World Literature},
  journaltitle = {Publications of the English Goethe Society},
  volume = {9},
  date = {1933},
  pages = {46--67}}
@Article{bertram,
  author = {Bertram, Aaron and Wentworth, Richard},
  title = {Gromov invariants for holomorphic maps on Riemann surfaces},
  journaltitle = {J.~Amer. Math. Soc.},
  volume = {9},
  number = {2},
  date = {1996},
  pages = {529--571}}
@Book{poetics,
  author = {Aristotle},
  editor = {Lucas, D. W.},
  title = {Poetics},
  series = {Clarendon Aristotle},
  publisher = {Clarendon Press},
  location = {Oxford},
  date = {1968}}
@Book{rhetoric,
  author = {Aristotle},
  editor = {Cope, Edward Meredith},
  commentator = {Cope, Edward Meredith},
  title = {The Rhetoric of Aristotle with a commentary by the late Edward Meredith Cope},
  volumes = {3},
  publisher = {Cambridge University Press},
  date = {1877}}
\end{filecontents}

\addbibresource{\jobname.bib}

\begin{document}
\chapter{First}
  \cites{companion}{rhetoric}
  \printbibliography[segment=\therefsegment,check=onlynew,heading=subbibliography]
\chapter{Second}
  \cites{companion}{bertram}{poetics}
  \printbibliography[segment=\therefsegment,check=onlynew,heading=subbibliography]
\chapter{Third}
  \cites{companion}{bertram}{gillies}{rhetoric}
  \printbibliography[segment=\therefsegment,check=onlynew,heading=subbibliography]
\end{document}

Results for the first chapter:

And the second:

And the third: