I am not sure if you are asking the cause of Mrs. Yeobright's death or if you are asking why Hardy chooses to have her die in the novel; so I'll answer both versions of the question.
1. Cause of death: Mrs Yeobright idolizes her son Clym and is, of course, unhappy when he chooses to marry such a controversial figure as Eustacia. After the marriage takes place, several events occur which serve only to strengthen Mrs. Yeobright's disapproval of her new daughter-in-law. One day, Clym's mother decides to travel to his cottage to make amends and to set things straight. However, Clym does not know that she has arrived at his door, and Eustacia does not open the door to her mother-in-law. When Mrs. Yeobright realizes that someone is inside and just refuses her entry, she leaves broken-hearted, believing that she has been rejected by her own son. She slowly tries to walk home but is overcome with the heat and her heavy heart. When she sits down to rest, she is bitten by an adder, and Clym later finds her, still alive, but she soon dies without knowing that her son did not reject her and, instead, tried to save her.
2. Hardy's choice to kill off Mrs. Yeobright's character: Mrs. Yeobright's death is simply another view of Hardy's fatalistic philosophy that Providence flirts with humans but does nothing to intervene on their behalf. The author would argue to his critics that it was Mrs. Yeobright's fate to arrive when her son was asleep and for her to be killed by the bite of an adder. Life on the heath is difficult and unforgiving, and Mrs. Yeobright's death not only exemplifies that truth but also serves to propel the tension between Clym and Eustacia, leading to the novel's tragic ending.
Among the three victims of Egdon in Hardy's novel, The Return of the Native, Clym's mother, Mrs.Yeobright, happens to be the first. On a hot and humid day of August, she walked a long distance to the cottage of her son to seek a possible reconciliation. Clym, serving as a furze-cutter, had been living with his newly-married wife, Eustacia.
In fact, Mrs.Yeobright unknowingly followed her own son to reach the cottage. But Damon Wildeve chanced to enter the cottage to talk to Eustacia as the tired mother chose to have some rest. When Mrs.Yeobright knocked at the cottage-door, her son was already fast asleep, and Eustacia was engaged in a conversation with Wildeve. So neither of them opened the door, and Mrs.Yeobright had to return, frustrated with the impression that her son had refused to open the door for the mother.
While returning all the way from Alderworth to Blooms End, the old exhausted mother was bitten by an adder. She was taken to a shed nearby and the rustics made efforts to save her by applying adder-oil. Even a doctor was being sent for. However, Mrs.Yeobright died broken-hearted, as much because of the adder-bite as being severely bitten by the idea that she was rejected by her only son, Clym.