Who do Catholics say the Mary in Matthew 27:56 is?

Question

Roman Catholics believe that Mary the mother of Jesus remained a virgin for her whole life. Mary the mother of Jesus is sometimes seen in the gospels with men referred to as Jesus' brothers, with names including James and Joseph. Then there's this verse:

Matthew 27:56 (NIV):

Among them were Mary Magdalene, Mary the mother of James and Joseph, and the mother of Zebedee’s sons.

Who does the Roman Catholic Church say this Mary (mother of James and Joseph) was? Were James and Joseph step-children (and therefore Jesus' step-brothers) or perhaps this is a different Mary altogether?

Answer 1

Different Mary, although James and Joseph were considered especially close to Jesus. They were called "brothers of Jesus" in the same vein as the word "brother" is used figuratively today: a bond of friendship close to that of family.

On Mary's perpetual virginity, the Catechism of the Catholic Church states (emphasis mine):

499 The deepening of faith in the virginal motherhood led the Church to confess Mary's real and perpetual virginity even in the act of giving birth to the Son of God made man. In fact, Christ's birth "did not diminish his mother's virginal integrity but sanctified it." And so the liturgy of the Church celebrates Mary as Aeiparthenos, the "Ever-virgin".

500 Against this doctrine the objection is sometimes raised that the Bible mentions brothers and sisters of Jesus. The Church has always understood these passages as not referring to other children of the Virgin Mary. In fact James and Joseph, "brothers of Jesus", are the sons of another Mary, a disciple of Christ, whom St. Matthew significantly calls "the other Mary". They are close relations of Jesus, according to an Old Testament expression.

501 Jesus is Mary's only son, but her spiritual motherhood extends to all men whom indeed he came to save: "The Son whom she brought forth is he whom God placed as the first-born among many brethren, that is, the faithful in whose generation and formation she co-operates with a mother's love."

Answer 2

The accepted answer succinctly nails it. To add a bit more information regarding it from the bible:

In the Gospel of John, we see that there are three people named Mary standing by the cross: the mother of Jesus, Mary Magdalene and Mary of Clopas. Furthermore, John tells us that Mary the mother of Jesus had a sister named Mary of Clopas (who was thus Jesus' aunt).

John 19:25: "but standing by the cross of Jesus were his mother and his mother's sister [adelphe], Mary of Clopas, and Mary Magdalene."

In the Gospel of Mark, we see a group of women looking on the cross from afar off, two of which are identified as Mary Magdalen and Mary the mother of James the less and of Joseph.

Mark 15:40: "And there were also women looking on afar off: among whom was Mary Magdalen, and Mary the mother of James the less and of Joseph, and Salome" [also referenced in Mark 15:47 and Mark 16:1]

In the Gospel of Matthew, we see a group of women looking on the cross from a distance, and three of which are identified as Mary Magdalene, Mary the mother of James and Joseph, and the mother of the sons of Zebedee.

Matthew 27:55-56: "There were also many women there, looking on from a distance, who had followed Jesus from Galilee, ministering to him, among whom were Mary Magdalene and Mary the mother of James and Joseph and the mother of the sons of Zebedee." [referred to as “the other Mary” in Matthew 27:61, Matthew 28:1]

Unifying these three gospel accounts, we see Mark and Matthew identify a Mary as the mother of James the less and Joseph. John records three people named Mary by the cross, and the only Mary of those three who would be fit to identify that way would be Mary of Clopas.

Thus, Mary of Clopas is identified as Mary the mother of James the less and Joseph. James the less and Joseph are thus cousins of Jesus. Jerome (383 AD) expands this argument to conclude that the adelphos of Christ named as James, Joseph, Simon and Judas (Matthew 13:55) are all four his cousins, likely children of Mary of Clopas.

If interested, this wiki breaks out that family tree in more detail, supplementing it with historical records.