I assume that you are talking about the seven virtues from the Catholic catechism. These are listed as:
Of these, there are are at least three that can be related to the idea that "those who mourn" are blessed.
First, justice is related to this beatitude. If we feel a strong sense of what is right and what is wrong, and if we always want people to be treated correctly, we will sincerely mourn those times when justice is not done.
Second, fortitude is related to mourning. When we truly mourn for the loss of a loved one or for the injustices of the world, we are intensely sad. But when we keep working hard for what is right and moral even in the face of this sadness, we show fortitude.
Finally, the idea of charity is related. This is similar to the relationship between justice and mourning. Charity can be seen as loving our neighbor as ourself. If we do this we will truly feel mourning when bad things happen to other people.