These epic axes will have the requirements you'll need to wield them and the stat bonuses for these weapons too. You'll find these in Titan Quest and Titan Quest Immortal Throne.

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These epic axes all have bleeding or attack speed bonuses. You’ll be able to tell that they are epic by the blue ink that they will have in the description.

Age Axe – This axe is not found in an item set, and it has an average speed with 85-95 damage. There are requirements of a character level of 32, a strength of 303, and a dexterity of 122. It has stat buffs of 27% pierce resistance, +19 to strength, +21 to dexterity, +40 to defensive ability, +10% to attack speed, and 10% chance of 102 bleeding damage over three seconds, 2 seconds of stun, or 28-43 bonus damage.

Beastrend – Not in an item set, this has an average speed and a 50-58 damage. There are requirements of a character level of 21, a strength needed of 211, and a dexterity requirement of 96. It has stat bonuses of +50% damage to beasts, +20% health regeneration, 16% bleeding resistance, 5% damage resistance, and 20% chance of +51% damage.

Sagaris Cocytus – Part of the Immortal Throne expansion, this axe has an average speed, 35% piercing ability, and damage of 66-76. It has requirements of a character level of 29, a strength required of 274, and a needed dexterity of 114. There are stat buffs of +18 to dexterity, +13 to strength, a 15% chance of 25 reduced resistance for two seconds or 99 bleeding damage over three seconds, and +16% pierce damage.

Creeping Death – This is not part of a set and it has 52-60 damage with an average speed. It has requirements of a strength of 239, a dexterity of 104, and a character level of 25. There are stat buffs of +10% attack speed, 84-108 poison damage over six seconds, 8% chance of +102% poison damage, 28% poison resistance, and +28 to offensive ability.

Bonehack – This axe is in the Immortal Throne expansion and it has an average speed with a damage of 63-72. There are requirements of a character level of 30, a strength of 274, and a dexterity of 114. There are stat buffs of +15% damage, 10% chance of 52 bonus damage, 29 reduced offensive ability for three seconds, 30 reduced armor for three seconds, +29 offensive ability, and +15% attack speed.

Skullcleaver – Not in a set, this has an average speed while bringing out 41-50 damage. It has a character level of 17 requirement, a needed strength of 183, and a dexterity requirement of 88. There are stat buffs of 50 reduced armor for three seconds, 12-16 piercing damage, +58% bleeding damage, and 12-27 bleeding damage over three seconds.

Now that you know the epics that have bleed and attack buffs, I hope that you can find one in the game. They will be random drops that can occur anywhere in the game.