Its all quite possible - I've used it a couple of times. There are many radio techniques that could be used - it depends on what is allowed in your country. You may not need much transmit power on the uplink – it depends on how clear the channel is on the airborne receiver.
The main consideration is that the cut-away device needs to be situated above the parachute - this means
that either the receiver and cut down driver circuitry needs to be small and light - or you situate it below the parachute and run wires up to the cut-down device itself. Be aware that long wires can be a bit of a hazard if the payload lands on a power line (it happens).
Depending on how you want to use a cut-away device you may want to consider speed of operation. If it's
just to detach from the inflated balloon then it doesn't need to be particularly fast. If it's to detach balloon remnants following burst then its best to have a fast device.
There are several techniques for the cut-down device – these are a few I've experimented with:
Hot wire and resistive cutters melt through the attachment line and need a reasonable amount of current –
they usually take a second or two to work. The current is a consideration for both the power source and the wire to the device itself. Don't forget you are trying to raise the temperature of the line above its melting point – from its airborne temperature which can be quite low (depending on the stage of the flight). Also consider the affect of low temperatures on the power source.
Servo – usually take less than a second to operate and don't need a lot of current. The cold can make
plastic gears and grease stiff – so you might want to consider warming the servo electrically before use. I've also noticed position drift due to the circuitry getting cold (depends on the quality of the servo). You may want to consider removing the grease or replacing it with something that is designed for low temperatures.
Pyrotechnic – these can be very quick at detachment and usually don't have large power supply requirements. They can often be fired reliably with a small capacitor (typically fire in less than 10ms with 1A). There may be health and safety/regulatory aspects to consider. These devices are usually expensive – but are very reliable and fast.
I've listed these techniques in increasing order of my preference – but its very much down to what
works for you. What ever technique you use I recommend a fair bit of environmental testing before flight.