Detectives are also examining possible links between the man, who is in his 40s, and the murders of Kate Bushell, a 14-year-old girl from Exeter, and Lynda Bryant, a 41-year old Cornish woman, who were killed in the past 14 months.
The suspect was arrested at about 6pm on Sunday in Torquay in connection with the attack on the mother and daughter in Netherton, near Newton Abbot, Devon.
The arrest followed the recovery of a Vauxhall Cavalier fitting the description of the car used by the attacker. Police said they found the vehicle in the Lichfield Avenue area of the town and were carrying out forensic science tests on it.
The 48-year-old woman and her 17-year-old daughter were assaulted as they walked their black labrador in a country lane near Netherton.
The attacker deliberately drove his car into the girl, knocking her down, according to the police. Mother and daughter were then driven to a field where the girl grabbed the man round the neck and the woman struggled to get out of the car. The man allegedly lashed out with a knife, badly cutting the woman's hands.
They ran to a house to raise the alarm, and the mother was taken to hospital in Plymouth where the wounds to her hands were treated. She may need plastic surgery.
Police later praised the pair for their bravery.
The man being held at Torquay police station was undergoing forensic science examinations yesterday and detectives are not expected to question him until later today.
Police are also examining similarities with two recent murders in the South-west.
Mrs Bryant, a mother of two, from the hamlet of Ruan High Lanes, was killed last October. She was seen talking to a man less than an hour before her body was discovered in a field. She was stabbed in the back, neck and throat.
Miss Bushell had her throat cut while walking near her home in Exeter, Devon, in November 1997.
Both victims were walking dogs along country lanes. In each case the motive is thought to have been sexual but there was no actual sexual assault. In the Bushell case the police are still looking for a light blue Vauxhall Astra van and in the Bryant case they are still searching for a white van.
A police spokesman said: "There has been liaison between the officers of the Newton Abbot offence and officers involved in the outstanding murders in Devon and Cornwall." He added: "They all involve a woman taking a dog for a walk along a country lane."
Police have also examined unsolved murders carried out in other parts of the country, but no links have yet been discover with the Devon and Cornwall offences.Reuse content