How does holy Baptism remind and assure you that the one sacrifice of Christ on the cross avails for you?

In this way: Christ has instituted this external washing with water and by it has promised that I am as certainly washed with His blood and Spirit from the uncleanness of my soul and from all my sins, as I am washed externally with water which is used to remove the dirt from my body.

What does it mean to be washed with the blood and Spirit of Christ?

It means to have the forgiveness of sins from God, through grace, for the sake of Christ's blood which He shed for us in His sacrifice on the cross, and also to be renewed by the Holy Spirit and sanctified as members of Christ, so that we may more and more die unto sin and live in a consecrated and blameless way.

Where has Christ promised that we are as certainly washed with His blood and Spirit as with the water of baptism?

In the Institution of Baptism which runs thus: GO YE THEREFORE, AND TEACH ALL NATIONS, BAPTIZING THEM IN THE NAME OF THE FATHER, AND OF THE SON, AND OF THE HOLY GHOST. HE THAT BELIEVETH AND IS BAPTIZED SHALL BE SAVED: BUT HE THAT BELIEVETH NOT SHALL BE DAMNED. This promise is also repeated where the Scriptures call baptism the water of rebirth and the washing away of sins.

I. Baptism Displays the Solution for Sin

A. Christ directed the believers to make baptism part of the gospel presentation and initiation into the Christian religion. Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost: (Matthew 28:19)

1. Baptism has always been for believers and their children. Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost. For the promise is unto you, and to your children, and to all that are afar off, even as many as the Lord our God shall call. (Acts 2:38-39)

2. Baptism marked the explosive early growth of the church. Then they that gladly received his word were baptized: and the same day there were added unto them about three thousand souls. (Acts 2:41)

B. The outward symbol of baptism points to a supernatural and internal operation of the Holy Spirit. I indeed baptize you with water unto repentance: but he that cometh after me is mightier than I, whose shoes I am not worthy to bear: he shall baptize you with the Holy Ghost, and with fire: (Matthew 3:11)

1. Just as sin is contagious, so is blessing. For I will pour water upon him that is thirsty, and floods upon the dry ground: I will pour my spirit upon thy seed, and my blessing upon thine offspring: (Isaiah 44:3)

2. God identifies Himself as the God of multigenerational grace. And as touching the dead, that they rise: have ye not read in the book of Moses, how in the bush God spake unto him, saying, I am the God of Abraham, and the God of Isaac, and the God of Jacob? (Mark 12:26)

C. Washing is an accurate illustration of the supernatural process underway in the gospel. The like figure whereunto even baptism doth also now save us (not the putting away of the filth of the flesh, but the answer of a good conscience toward God,) by the resurrection of Jesus Christ: (I Peter 3:2 1)

II. Cleansing from Sin Comes by Grace

A. It is the blood atonement, not the external process, which accomplishes the necessary cleansing. In whom we have redemption through his blood, the forgiveness of sins, according to the riches of his grace; (Ephesians 1:7)

B. The pouring process points to the outpouring of the Holy Spirit which effects the changes Which follow the atonement. And such were some of you: but ye are washed, but ye are sanctified, but ye are justified in the name of the Lord Jesus, and by the Spirit of our God. (1 Corinthians 6:11)

C. The pouring process also points to the relationship of Christ and the Holy Spirit in the redemption of sinners. And I knew him not: but he that sent me to baptize with water, the same said unto me, Upon whom thou shalt see the Spirit descending, and remaining on him, the same is he which baptizeth with the Holy Ghost. (John 1:33)

III. Baptism in the Spirit Is Critical

A. Baptism is a life and death matter. He that believeth and is baptized shalt be saved, but he that believeth not shalt be damned. (Mark 16:16)

1. Baptism does not guarantee salvation in itself. Those by the way side are they that hear; then cometh the devil, and taketh away the word out of their heart, lest they should believe and be saved. (Luke 8:12)  

2. The new birth is God's work, not the sacrament's work. But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name: Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God. (John 1:12-13)