Mental health charities have been quick to condemn Clarkson's comments, particularly after the tragic death of Wales manager Gary Speed last week.
Writing in his column in The Sun on Saturday, the Top Gear presenter claimed that people who kill themselves on railways cause "immense" disruption to the journeys of commuters.
He said: "I have the deepest sympathy for anyone whose life is so mangled and messed up that they believe death's icy embrace will be better. However, every year around 200 people decide that the best way to go is by hurling themselves in front of a speeding train. In some ways they are right. This method has a 90% success rate and it's extremely quick.
"However, it is a very selfish way to go because the disruption it causes is immense. And think what it's like for the poor train driver who sees you lying on the line and can do absolutely nothing to avoid a collision."
Later in the column, he described people who jump in front of trains as "Johnny Suicide", and called on trains to just continue their journey after the death, leaving the body parts to scavenging animals.
Mind chief executive Paul Farmer hit out at the "extraordinarily tasteless" views expressed in The Sun column, which he said showed "an utter lack of understanding of the tragedy of any suicide".
He also confirmed that Mind and fellow mental health charity Rethink Mental Illness would ask the Press Complaints Commission to investigate his comments.
"Every single suicide is a tragedy, and there is an important debate to be had about railway suicides," said Farmer in a statement on the Mind website.
"Our colleagues at Samaritans have an excellent partnership with Network Rail and have already helped to reduce the number of suicides on the railway through sensitive, but focused work.
"Sadly there is still a great deal of stigma and misunderstanding about suicide and mental health problems. The fear of people's reactions can make it incredibly difficult for people to come forward and seek help and this can have tragic consequences.
"Any celebrity, even Jeremy Clarkson, has a responsibility to be cautious when discussing a sensitive topic like suicide in the media. There is evidence from research in the UK and around the world that media representations of suicide can and do lead to copycat behaviour. The media has a duty of care to present suicide in a responsible way."
Mental health charities Sane and the Samaritans have also criticised the comments.
Clarkson's controversial comments on suicide follow last week's controversy over statements he made on BBC One's The One Show that striking public sector workers should be shot.
The 51-year-old was forced to apologise for the comments, which generated more than 21,000 complaints and prompted trade union UNISON to call for him to be sacked by the BBC.