Hi,
The "brute force" method is a relay, but that's bulky, not power efficient, relatively expensive and strictly, needs an overswing protection diode, so involves two components. The smallest method would probably be an optocoupler (4 pins?), but that probably requires a resistor for the LED so still two components, inefficient and limited current capability.
For moderate currents in the PICaxe, then almost any CMOS gate package could control the supply or earth rail of the PICaxe. Cheap, but the gate package is likely to have 14 pins. For higher currents (e.g. if the PICaxe drives lots of LEDs) then a cheap NPN + PNP transistor pair and a few resistors could switch the PICaxe rail economically, but obviously not a minimum component count.
However, all these "solutions" require one or more additional components wired across the battery. So, as geoff has already said, in most cases it's probably best to just keep the PICaxe connected to the battery and simply minimise its current drain with SLEEP and DISABLEBOD, etc. commands. Then wake it up with a power cycle.
Cheers, Alan.