The Idea in Brief
The apparent reading is that blood cleanses from sin, but that water provides complete cleansing in respect to the removal of death (covenant separation).
In the Hebrew Bible, blood atones for sin, but it is water that washes away death. This washing away therefore restores one to covenant relationship to the Lord. In this respect, Jewish oral tradition as found in the Babylonian Talmud indicates that not all things are cleansed with blood; that is, water complements blood atonement by washing away covenant separation from the Lord, which is "death."
The key to understanding this passage lies in the verses in the immediate context preceding.
Hebrews 9:19-22 (NASB)
19 For when every commandment had been spoken by Moses to all the people according to the Law, he took the blood of the calves and the goats, with water and scarlet wool and hyssop, and sprinkled both the book itself and all the people, 20 saying, “This is the blood of the covenant which God commanded you.” 21 And in the same way he sprinkled both the tabernacle and all the vessels of the ministry with the blood. 22 And according to the Law, one may almost say, all things are cleansed with blood, and without shedding of blood there is no forgiveness.
NOTE: The highlighted words come from Exodus 24:8.
The shedding of blood provided for forgiveness; however, complete cleansing only comes with water, which washes away death--for example, the once dead flesh on the leper was sanctified by water (Lev 14:4-7); and of course the recipe for cleaning people contaminated by things dead was the water filtered through the ashes of the red heifer (Nu 19:1-22).
The writer of the Book of Hebrews in this very context made allusion to Exodus 24:3-8 (ref: highlighted words in the verses quoted above), where Moses sanctified the book of the covenant with blood. That is, the author of the Book of Hebrews indicated that there was not only blood involved, but also water (although the water has no explicit mention in the context of Exodus 24:3-8), since we read "...water and scarlet wool and hyssop..."
The writer of the Book of Hebrews therefore appears to have been familiar with Jewish oral tradition, which is captured by the Jewish Talmud, and, according to the translation by Neusner (2011), the Babylonian Talmud makes the same assertion in Yebamot Folio 46B. That is, although Exodus 24:3-8 makes no mention of water, Jewish oral tradition indicates that water was, in fact, involved within the context of conversion (baptism). That is, the Talmud indicates that water cleansing brought the convert into living covenant relationship with the Lord.
The writer of the Book of Hebrews recognizes Jewish oral tradition in that the scope of Exodus 24:3-8 was not limited to blood, but to water as well. This living water washed away death. That is, while blood atoned for sin, it was water that washed away the death (covenant separation) from the Lord. In this respect, the writer of the Book of Hebrews is careful to say ALMOST all things are cleansed with blood. The reason is because blood (which stems from death) does not wash away death: water instead is the agent for washing away death, and thus provides for complete cleansing and restoration of covenant relationship with the Lord, which brings life.
Neusner, Jacob (2011). The Babylonian Talmud: A Translation and Commentary (Vol. 8). Peabody: Hendrickson, 236-237.