A mine in space will be something like a CAPTOR sea mine. Since space is vast, and you will have limited resources, the reason for having a "minefield" will be to deny access to something valuable, which is most likely a planet.
To do so, you will need to have your mines in orbit around the planet to make it difficult for enemy spacecraft to orbit your planet. This can be done in many different ways; the least sophisticated (and probably most expensive in terms of mass and lift) would be to fill LEO with all kinds of space junk. Particles of sand or ball bearings whining around the Earth at 7 km/sec would have a huge amount of kinetic energy relative to their size (An object impacting at 3 km/sec delivers kinetic energy equal to its mass in TNT. This is often known colloquially as "1 Rick" of energy). An incoming ship wold be effectively pelted with hand grenades and have sensors, radiators and other "soft" equipment rapidly stripped away.
The disadvantage of this minefield is it is going to be difficult and expensive to clear it, both for the attacker, and equally for you, should you need to launch your own spacecraft. If the "field" is in polar orbit, you effectively block both incoming and outgoing flight from the entire planet.
Captor type mines get around this problem by orbiting in defined paths, but having sensors and the ability to launch offensive weaponry at the target (A CAPTOR mine houses a torpedo). A simple form of this would be mines carrying missiles to launch at the target when it comes into range. Since multiple mines could be in range at a given time, the enemy ship suddenly has to deal with a saturation attack.
More advanced forms of this would exchange the missile bus for a nuclear warhead. Following the Atomic Rockets "Conventional Weapons" site, nuclear explosives can drive high velocity kinetic or energy attacks against spacecraft. This not only puts the craft at risk from long distances, but the extreme velocity of the projectiles ensures there is no left over space junk near your planet (although the objects will continue to move through space until something stops them in the future).
Nuclear explosions can drive "shotgun" pellets at 100 km/sec
Nuclear shaped charges which can drive slugs of liquid metal at up to 3% of the speed of light
Casaba Howitzers which are specialized shaped charges which emit a star hot spindle of plasma at 10% of the speed of light (enough speed and energy to be comparable to very powerful laser weapons at hundreds to thousands of kilometres away without a heavy and expensive laser generator.
Conceptually, nuclear explosions can also drive X ray lasers, providing huge energy dumps on a target at the speed of light.
Weapons like this extend the reach of a "mine" to distances from hundreds of kilometres to up to a light second (after that, light lag means the enemy spaceship has ample opportunity to evade incoming strikes).
Remember, mines are automated systems, so the enemy could spoof them or discover a means of disabling them. Alternatively, he could choose to sacrifice some ships (perhaps empty hulks) to discharge enough mines to create a clear space to operate. As mines become more sophisticated to deal with this, their advantage of being numerous and inexpensive declines (although they will still be far cheaper than spaceships with comparable weapons load outs).