I don't know much about your ships like if they have FTL drive, shield, lasers, sub-light speed, etc but I'll try to make "universal" answers.
If you don't want to damage the ship you could try to hack them, ships has comunication sytems so you could try entering to their system by the comunication console. In Battlestar Galactica cylons used to hack humans ships to destroy them.
If a remote hacking by comunication console seems impossible you could make a little dron, this dron fly to the enemy ship, attach to their armor, search for a console or data cables, connect to them and start hacking. By radio or Wi-fi you comunicate to the dron and the dron hack the ship.
If you want be able to support the hacking you simply need a better firewall or programmer. Also you can do like in the series, in Galactica the main ship (I forget the name) used cables to connect the sub-networks of the ship and when they was under a hacking attack they simply unplug the network cable.
Ultra powerful magnetics turrent can "fire" an electromagnetic wave. You can use two ways to desactivate enemy ship:
- Increase "slowly" (in 10 seconds) the power: You can make an annoying electromagnetic wave, harmless to electronic circuits but it increase his power all the time. The enemy ship would have to desactivate the circuits in order to not destroy them when the magnetic field become too powerful. Surrender or EMP.
- Have an "electromagnetic shower": making a big and powerful EM wave you can "blind" the target, EM distrub communications, radar and even targeting systems, the ship would be incomunicate and blind. ¿Would you enter into the hyperspace or a wormhole blind?
- A third way could be increasing the static energy of the ship by gamma ray, if the static is to high it will break technology and even kill the crew (in space static is a real danger). The only problem is that I see that in a sci-fi series and I don't know if that is possible.
Also, if you think that a EM turrent is too powerful or strange you can insted have mini drones that fly around the enemy ship and make the EM field.
Ally ship (a big one) could launch hundreds of little drons, they attach to the enemy armor (by steel ropes or hooks) an fly to the opposite side. A lot of them would stop the ship, the problem is that you need a lot of them and they have low fuel storage also.
Ship Roop Tying
If you don't like drons you can have a lots of steel ropes launchers. They launch the ropes to the enemy and them attach to the ship, then your allies ships stops the enemy with they own thrusters.
Destroy the Thrusters
If enemy ship has ion-thrusters, EM thrusters, gravitional drives or something like that you can shoot to their thrusters, I don't think they will blow up, right?
By a laser or microwaves you can heat enemy ships (in space ships doesn't cold down so easy). If the ship reach to a critical temperature the fussion reactor would turn off to avoid explode. Also people can die "cooked" or by deshidration.