What is mortal sin? Is agression a mortal sin? What is a mortal sin? Is physical or verbal agression to a family member, father, brother, sister, mother, uncle, cousin, aunt or friend a mortal sin. What are the effects and can it be forgiven and in what way?

Thanks.
From Wiki we learn:


  A mortal sin (Latin: peccata mortalia), in Catholic theology, is a
  gravely sinful act, which can lead to damnation if a person does not
  repent of the sin before death. A sin is considered to be "mortal"
  when its quality is such that it leads to a separation of that person
  from God's saving grace.
  
  ...
  
  
  Its subject matter must be grave.
  It must be committed with full knowledge (and awareness) of the sinful action and the gravity of the offense.
  It must be committed with deliberate and complete consent.
  


And from BeginningCatholic.com we read:


  … a single act of mortal sin is a bold declaration that you do not
  accept God’s love.
  
  Mortal sin destroys charity in the heart of man by a grave violation
  of God’s law; it turns man away from God, who is his ultimate end and
  his beatitude, by preferring an inferior good to him…. Mortal sin is a
  radical possibility of human freedom, as is love itself. It results in
  the loss of charity and the privation of sanctifying grace, that is,
  of the state of grace. If it is not redeemed by repentance and God’s
  forgiveness, it causes exclusion from Christ’s kingdom and the eternal
  death of hell, for our freedom has the power to make choices for ever,
  with no turning back. (Catechism, 1855 &amp; 1861; The entirety of Catechism section IV is of great value here and should be read carefully.)


From these perspectives, verbal aggression COULD be a mortal sin IF the aggression is remarkably substantial, the perpetrator is fully aware that he/she is comitting a mortal sin, and the action is not spontaneous nor an act of passion, but is deliberate --- even planned.

That describes a remarkably evil person, but in my experience, the vast majority of people who are verbally aggressive are no where near comitting a mortal sin (though a sin, certainly, Matt 18:6 and Matt 18:3-4).  However, perhaps the most important aspect is this line of the Catechism...


  If it is not redeemed by repentance and God’s forgiveness...


A mortal sin is something that must either be declared by the authority of the church, or judged by the Lord after death.  Therefore, the simplest answer to your question is "no."

As for forgiveness, that begins with repentance, which begins with stopping the sinful behavior.

If your circumstance or the circumstances of someone you know led to this question, I strongly recommend contacting your priest/pastor.