This event occurs in Act IV scene 3 of this great tragedy. Brutus gives a typical stoical response, in contrast to Cassius, when he tells him that he has received news of his wife's death. According to him, Portia killed herself because she was missing Brutus so much and also she had heard news that the opposition against him was now so strong, she became distraught and "swallowed fire" when her servants were not at home. According to Plutarch, she killed herself by putting hot coals in her mouth.
However, what is interesting is the way that Brutus chooses to supress all emotion and carry on with the job at hand. Note what he says:
Speak no more of her. Give me a bowl of wine.
In this I bury all unkindness, Cassius.
In a short sentence he dismisses her as if she never existed and goes on to make peace between himself and Cassius. This of course is questionable, but a lot depends on the individual director as to how they would stage this scene. Some would have Brutus showing some form of emotion, at least in private, or perhaps barely being able to master himself. It depends a lot on how sympathetic you want the audience to feel for Brutus at this stage of the play.
According to Brutus, Portia committed suicide because she missed her husband and was worried about Mark Antony’s and Octavius’ increasing power and authority. Their new found status increased the threat to Brutus and his friends.
Impatient of my absence,
And grief that young Octavius with Mark
Have made themselves so strong: for with her death
That tidings came: with this she fell distract,
And, her attendants absent, swallow'd fire.
Historically, Portia’s death remains contentious, with different accounts of how she died. The accounts state that she either swallowed hot coals or died of carbon monoxide poisoning or some illness.
Brutus seems to react calmly to the news as he talks to Cassius. He asks that they don’t speak any further about Portia’s death. His reaction can be seen as some form of coping mechanism expected of a man of Brutus’ character. Brutus is trying to demonstrate his strength in the face of great odds. However, it should be noted that he loved his wife dearly and such news definitely touched him.