Heb 9:13 For if the blood of bulls and goats and the ashes of a heifer, sprinkling the unclean, sanctifies for the purifying of the flesh, 14 how much more shall the blood of Christ, who through the eternal Spirit offered Himself without spot to God, cleanse your conscience from dead works to serve the living God?

 

Not just cleansed FROM, but TO. To what? The same Greek word here translated serve, is used again in Heb.10:2 to further define the discussion. "...For the worshipers, once purged, would have had no more consciousness of sins." A derivative of the same word is used in 9:1 AMP "The first covenant had its own rules and regulations for divine worship." 
Heb 9:15  And for this reason He is the Mediator of the new covenant, by means of death, for the redemption of the transgressions under the first covenant, that those who are called may receive the promise of the eternal inheritance. 

Bottom line: purged from dead works to worship! ...And the benefit of that worship? "No more consciousness of sins." Therefore, what the blood of Jesus accomplished, the worshipers' heart maintains. There is no sin consciousness or appetite in the presence of God! "Dead to sin" requires encountering His Presence!