Melee
Axes
Axes are a chopping tool perfectly suited for separating things from other things. Usual combat axes are usually way smaller than what fiction depicts. This is because the larger the axe head, the heavier it is, the harder it is to use it for a prolonged time. But you might want bigger axe heads in your situation, because it also means easier to chop off whatever it hits.
This also means that axes will have to be employed more tactically than just a straight "go and smack people". You want to make each attack count. In that regard, you probably want to set up ambushes and/or distract the enemies before sending some people to axe them some questions. Try to blind and confuse them, or flashbangs, just general explosives (very loud, very distracting).
Do not bother with poleaxes and similar "long handle axe" weapons. They are good for hitting people from afar, if the other person wields a melee weapon. But are not really great at hitting them accurately. If you want fast maiming, use an axe. However, if you have a dedicated limb removal squad, you can have some members of it have some means of restraining a victim. Lassos, bolas, and even some polearm-type weapons. Maybe something as simple as what dog catchers use (a long stick with a loop at the end) or even a very long hook. Idea is to take down the target and have them as immobile as possible to allow axe wielders to attack more easily.
If the setting has them, stun guns are also going to be quite useful to give axe wielders an opportunity. Squad members can easily have both a taser and axe equipped.
Cleavers
Similar to axes, it is a chopping tool. It is less effective than axes (smaller, less power when swinging it) but it is more portable. Any soldier can carry one. And can serve as a replacement of (or addition to) a regular knife. More of an opportunity weapon but if you really have to dismember enemies often, it might be useful for everybody to pack a cleaver just in case.
Machettes
Also hacking weapons. Bigger than a cleaver, not quite an axe. Still an effective weapon if your aim is chopping.
Ranged
There is not much quite suitable for removing limbs in ranged weapons. It is usually an unreliable method of taking down an enemy - normally, you want to shoot at the centre of mass or at the head. Both would stop an attacker immediately. Most other shots are not guaranteed to disable an enemy, not to mention, it is also a lot harder to aim for limbs. Hence nobody has focuses on "arm chopping guns" or similar.
Various games have still tried. Unreal Tournament has a gun shooting razor sharp disks, Half-Life 2 allows you to shoot saw blades at people, Painkiller has a weapon that shoots shurikens and lightning, etc. However, they all essentially run on magic and generally mass producing these is going to be massively expensive and all sorts of logistic nightmare. Just imagine a crate of bullets - it can probably hold a thousand. The same crate can probably fit ten-ish disks for the Unreal Tournament razor gun.
Shotguns with less lethal ammunition
Assuming the aim is not to kill the enemy, your best bet might be to try and stun and/or disable them. Then move in with something more suitable. Like an axe.
There is no official "non-lethal" ammunition. Rubber bullets and other rounds that are not specifically designed to kill are called "less lethal". They can still kill if they hit some vulnerable spot. However, less lethal ammo does have good stopping power. However, the bigger the thing hitting the enemy, the better. Rubber bullets can hurt, sure, but shotguns can fire really big and heavy rounds that are almost guaranteed to stop an enemy. You probably do not care for any permanent damage from these rounds, so they can be employed liberally.
Less lethal grenades and other larger projectiles
Technically, the same thing as shotguns. However, there are less lethal projectiles designed to be shot from 40mm grenade launchers. There are also other guns that can shoot big things. This includes guns that quite literally can shoot a can of Coca-Cola (or anything shaped like it). Also potato cannons that can shoot potatoes (as the name suggests). But you probably want some projectiles that are more designed for aerodynamics.
These types of less lethal ammo should deliver a bigger punch than what a shotgun does. But also require more powerful guns to be shot with. You probably want something like this for longer range.
Lethal option - explosives
This is going to be tricky, mostly because there is a high chance the enemy does not survive. But if you do not particularly care, then just shoot them with explosives.
Assuming you want to make at least an attempt at capture, then do not shoot them with a rocket. Instead, you want something like FRAG-12 - it is a shell fired from a shotgun (specifically the AA-12) which explodes on impact. See demonstration on YouTube. This is very much not less lethal. But if you face soldiers that can regenerate in seconds, then they might be able to take few shots from this. There is probably not going to be too much of the body left where it hits, so try to aim for the limbs. And maybe hope that if you hit the body elsewhere, the enemy would survive.
Other
Mines and booby traps
This can probably help if backed up by an ambush. But you can set up traps for the enemy. A mine can ruin a legs, but you should follow this up with soldiers nearby attacking the poor victim while down.
Biologically active substances
In other words, pump the enemies with drugs. Not the lethal kind but any agent that can make the enemy less effective.
Sleeping darts are a definite option.
You can also shoot enemies with hallucinogenics. If they really are quite powerful, that can be a way to wreak havoc at the enemy lines, if some of the enemies start behaving erratically. Maybe even attacking their friends.
Parasitic agents can aid in capturing enemies.
Stun guns of all varieties
I mentioned tasers before but it still bears its own section. You can zap enemies with electricity from close range or longer range and incapacitate them for long enough to get into position and do something else.