It's hard to beat a simple jigsaw, but some precision abrasivejet systems are being used to cut wood, typically for special intricate shapes and only after delivering a return on investment via metal parts production.
Because wood is very soft compared to metals, the abrasivejet machines it very quickly.
The first waterjet cutting experiments in the USA were done by Norman Franz on wood in the late 1960s. However, there have been no commercial applications of log cutting because the cutting performance drops off quickly with thickness. Abrasivejets are very practical for cutting shapes in veneers and plywood up to 1/2" (1.3 cm) thick.

Wood parts (courtesy Redekop Mfg. Ro, Saskatoon, Canada)

Airborne industries parts
This dragon is made from 1/2" (1.3 cm) thick pine
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