Grineer Specific

(4 Forma. Alternatives might increase the need.)
(Also works for other armored enemies, but you'll have to switch the Smite Mod.)

Q:Why no Viral?
A: [Panzer Vulpaphyla] and other ways of priming enemies exist. Primed Smite increases proc damage by 1.55x1.55 = 2.4025x. Roughly the value of 3 Viral procs in one mod. The performance is rather similar, but once you factor in outside Viral procs, Primed Smite always wins by far. It also opens up another mod slot that can be used for more attack speed or other forms of DPS.
(Why the hell wouldn't you use [Panzer Vulpaphyla]? Get that weak ass smeeta out of here.)

Q:Why no Heat?
A: Are you stupid?

Q:Why no Elemental mods at all? The DPS is so tiny!
A: Grineer don't care about your DPS as long as they have armor. They only care about slash procs (Unless you bring a ridiculous amount of damage, like with a melee [Saryn]), so our goal is maximising slash proc damage. Elemental mods don't increase slash proc damage.
If you armor strip them, feel free to build pure Viral, but realistically armor stripped Grineer are a joke anyway and fall to unmodded Skanas.

Q:But Berserker is bad now?
A: 70% > 55%. Getting a quick kill to get Berserker started is easy. Abuse the forced knockdown of the slam follow-up and do a ground finisher if there are no weak enemies around. Once you get killing you likely won't stop killing. Also, [Gladiator Vice] and Arcane Strike exist.

Q:Why [Blood Rush]? 15% crit is bad!!
A: 15% Crit still gets you 81.1%, with a multiplier of 3.6x. These two mods alone increase DPS massively without gimping slash damage like elemental mods would.
[Gladiator Vice] increases that to 97.6. Alternatively, if you do not need [Gladiator Vice]'s attack speed, [Sacrificial Steel] is a nice DPS increase. This is especially true if you use Arcane Strike or a frame buff for more speed.
Alternatively alternatively, if you don't need more crit chance, [Quickening] provides slightly more attack speed, but no crit chance.

Q:But where is the Combo Duration?
A: Naramon Focus, Primary Dexterity, Secondary Dexterity, [Swift Momentum] or even [Ash]'s [Rising Storm]. Modding Combo duration on the melee is a wasted mod.

Q: [Condition Overload] or [Primed Pressure Point]?
A: [Primed Pressure Point] if you use this build without outside procs on weaker enemies. On stronger enemies and with [Panzer Vulpaphyla] or other extra procs, [Condition Overload] wins.

Q: What about [Carnis Mandible]? [Gladiator Might]?
A: Very much a possibility. Right now our average Slash procs per hit are at 0.845. With [Carnis Mandible] we would hit 1.166. A significant jump in reliability, but we lose dps as +Slash mods do not increase slash proc damage. So it is a decision to be made between Glad.Vice/[Sacrificial Steel]'s DPS versus having slightly more slash procs per hit, which also increases DPS.
Without Arcane Strike, [Gladiator Vice] provides +17.6%. 0.845*1.235= 0.9937. Less slash procs over time than with [Carnis Mandible], but the attack speed adds another factor of usability, as well as the extra critical chance making you hit 97.6%, further increasing the value of slash procs on average to around ~1.131 procs worth. That is still slightly less than Mandible, but faster Attack speed also means we get more forced slash procs from the stance, making [Gladiator Vice] ultimately better than [Carnis Mandible] if you don't use other sources of attack speed, like Strike or frame buffs.
[Sacrificial Steel] would increase the value of those 0.845 slash procs by 55.3% on average. = 1.31228. So that would technically be the best option for DPS, at the cost of usability and one more Forma. If we don't already use a load of Gladiator mods on the frame or other critical chance buffs.
[Gladiator Might] on the other hand also gives us the critical chance buff as well as a critical damage increase. This is slighly weaker than [Sacrificial Steel] on average (but more consistent), and stronger than [Gladiator Vice] at the cost of some attack speed.
What you value more is your decision and it heavily depends on what else you bring along you to the mission. I personally felt that only Berserker for attack speed doesn't feel good enough, so my choice was [Gladiator Vice]. But with Arcane Strike on the frame or an attack speed buff, [Gladiator Might] would be my choice.

The weapon still sucks compared to the competition, but it can still rip those Steel Path Grineer apart.
A way to gather enemies to abuse the perfect follow_through is also recommended, but not necessary.

Oh, and you can just use this exact build on any Slash viable melee weapon. You'll be more likely to use [Gladiator Might] instead of Vice though.