If you have your A3 document finished, compile it to a PDF and include it into a new A4 document which uses pdfpages to include the A3 page twice with first the right, then the left half clipped away. pdfpages will take care of removing all borders etc.
\documentclass[a4paper]{article}
\usepackage{geometry}
\usepackage{pdfpages}
\begin{document}
\includepdf[pages=1,clip,trim=0 0 21cm 0]{example-image-a3-landscape}
\includepdf[pages=1,clip,trim=21cm 0 0 0]{example-image-a3-landscape}
\end{document}
(The example image example-image-a3-landscape.pdf is part of the relative new mwe package.)
This looks the following way in the side-by-side view of Adobe Reader:

As already pointed out you might run intro trouble if your printer can't print to the very edge of the page, which is usually the case with a normal printer!
So you might want to let about 1cm margin on top and bottom and 2cm on the left and right of the A3 paper. Then you can remove 1cm on every side of each A4 page by changing the trim values. You need to disable auto-scaling and page-fitting as well (always a good idea in such cases anyway). I added frame so you can see the real content size easily. You should remove this key for the final version.
\documentclass[a4paper]{article}
\usepackage{geometry}
\usepackage{pdfpages}
\begin{document}
\includepdf[pages=1,clip,trim=2cm 1cm 21cm 1cm,frame,noautoscale,fitpaper=false]{example-image-a3-landscape}
\includepdf[pages=1,clip,trim=21cm 1cm 2cm 1cm,frame,noautoscale,fitpaper=false]{example-image-a3-landscape}
\end{document}

TikZ(and A3-to-A4 typeset/print questions). – Alenanno May 21 '12 at 14:48trim left=....andtrim right=...to shift the picture out of the page. – percusse May 21 '12 at 15:11