List of Pure-Damage Heroes by Role

The following heroes have one or more abilities that deals Pure damage, or deal pure damage with an Agh's upgrade.

Also shown on dota2pedia in a different format.

Pure Damage Dealers by Role (ability)

Carries

• Outworld Destroyer (Arcane Orb)
• Phantom Assassin (Stifling Dagger)
• Spectre (Desolate)

Semi-Carries & Mids

• Silencer (Glaives)
• Invoker (EMP, Sunstrike)
• Lina (Agh's + Laguna Blade)
• Bloodseeker (Rupture)
• Phoenix (SunRay)
• Pudge (Meat Hook)
• Templar Assassin (Psi-Blades)
• Tinker (Laser)

Supports

• Lina (Agh's + Laguna Blade)
• Bane (Nightmare, Brain Sap)
• Omniknight (Purification)
• Phoenix (Sunray)
• Silencer (Glaives)
• Vengeful Spirit (Wave of Terror)

Initiators

• Doom (Doom)
• Enigma (Midnight Pulse, Aghs + Black Hole)

Junglers:

• Enchantress (Impetus)
• Doom (Doom)
• Enigma (Midnight Pulse, Aghs + Black Hole)

Solo Offlaners:

• Timbersaw (Whirling Death*, Timberchain, Chakram)
• Nyx Assassin (Spiked Carapace)
• Doom (Doom)

ITEMS that deal pure damage:

• Urn of Shadows (on enemy)
• Blademail (Damage return)

Composite Damage

Composite damage was a mechanic where damage could be both physical and magical, and both armor, damage block and magic resistance applied to it, but it could damage magic-immune target, but does not affect ethereal units.

Composite damage will be removed in Dota2 patch 6.82.  The heroes that had composite damage abilities prior to that patch included:

Leshrac - Diabolic Edict (changing to Physical)
Beastmaster - Wild Axes (changing to Physical)
Alchemist - Acid Spray (changing to Physical)
Techies - Land Mine (changing to Physical)
Lone Druid - Backlash upon death of Bear (changing to HP Removal)

... and HP Removal is no longer a "Damage Type", but a side-effect of using certain hero abilities (e.g. Huskar Burning Spears).

From the dota2 wiki:
** Composite damage is calculated by multiplying the initial damage by the target's magic resistance and armor. For example, if you had 25% magic resistance, 50% physical damage resistance, and stepped on a full damage Level 4 Land Mine, the equation would be 600 x 0.75 x 0.50 = 225 actual damage. (Magic resistance and physical damage resistance percentages are subtracted from 100%.)