The simplest solution would likely be to make a Redstone Clock with enough Repeaters to have the clock cycle every minute. Repeaters can be set delays from 1 to 4 ticks, and each tick lasts 0.1 seconds, so you would need 150 Repeaters set to their full delay to last for one minute. Keep in mind that Redstone signals take 1 tick to propagate through Redstone Torches, so if timing is extremely important you will need to take this into account and adjust the timing of your Repeaters accordingly.
Alternatively, if you have enough space to create an area with no risk of entities obstructing the path, you could use a Minecart-based clock, with a detector rail connected to a T Flip-Flop as the output of the circuit. Minecarts travel at 8 metres per second at their top speed, so you would need a track 480 rails long to create a 1 minute delay (assuming the Minecart is moving at its top speed the entire time). This doesn't take into account the fact that Minecarts move faster along diagonals, so the Minecart would technically be traveling at 11.314m/s at any corners in the track. If the timing of the circuit is important, this will make the timer inaccurate after many loops of the clock. Also, this design would add complexity if you needed to be able to start and stop the timer.