As far as I am aware there were no original compositions for the musical saw until after the 1900's. Perhaps this was because the instrument had been previously associated with the music hall and not regarded as a classical instrument.  The instrument started  to become an established classical instrument in the 1920's  with a greater concentration of compositions much later on in the 21st Century.  

The following is a list of original works for the musical saw in order as they appeared from the start of the 20th Century.   I'll add to this lisat as my research continues and please let me know if you've discovered any other pieces for the musical saw .

Stravinsky’s Oedipus Rex (1927) uses the musical saw to track the song of the Sphinx whilst she taunts Oedipus with a quarter-tone declamation.

George Enescu's opera Oedipe (1936). It is big in length, big in orchestral and choral resources, and big in theme - no less than the whole life story of Oedipus, from birth to death. Enescu uses every device he can lay his hands on; there are tubular bells, a wind machine, a musical saw , two pistol shots, and a recording of a nightingale. The singers, as well as singing, speak, shout, groan and gasp and, on one occasion, gives out a bloodcurdling scream. 

Henri Sauguet   wrote a piece called  “Plainte” (1949) for musical saw and piano.

Malcolm Arnold in 1953/54 wrote the score for the film Hobson's Choice. This was based on Harold Brighouse play and was set at the turn of the 20^th Century. Malcolm  used his recollections of Parlour-music based on a 22 member pit orchestra and this finds its way into the score. Arnold ’s favourite scene in the film is Hobson’s moon dance. After the music stops a musical saw is heard magically conveying the sense of the moon’s reflection  shimmering in some water. The performer was Jacques Louisser,  who was a Belgian Café owner and he was persuaded to come and play at a considerable expense.

Charles Chaplin in 1959 wrote music scores written after his exile from the United States when Chaplin  had the opportunity to spend more time composing. He wrote music for the 1918 film  A Dog's Life  scored with the following instruments : Flutes, Oboe, clarinets, Bassoon, Horns, 3 Trumpets, 2 Trombones, Tuba, Harp, Guitar,
Musical Saw, Piano, Strings, Percussion.

Alfred Schnittke's Nagasaki Oratorio (1957–58,)- Was written in the era of the cold war. The Independent referred to this piece ( 27th Aug 2009 ) as "bombarding the audience with everything in his orchestral armoury" and that of course includes the musical saw.

Penderecki’s Capriccio for violin and orchestra (1967)  includes hummed vocalisation, electric guitar and musical saw.

George Crumb included a saw in his “Ancient Voices of Children. (1970)” 

Penderecki’s De Natura Sonoris II. (1971) features dramatic glissandos, dense clusters, and a use of harmonics, and unusual instruments such as the musical saw.   

Jonathan Rutherford  wrote an " Intake of Breath" (1999) (for musical saw, violin and soprano) available from http://www.modusmusic.org/ was first broadcast in April 2001 on BBC Radio 3.

2001

Peter Wiegold  wrote the 'Angel of Night' (2001) for musical saw vibraphone, flutes, bass clarinet and double bass .

Jonathan Rutherford  also wrote a Double Concerto for Accordion and Saw (or flute) with string quartet (2002) This is a substantial 45 minutes long piece and  was written for Owen Murray and Harriet Longman. This  can be heard in computer generated performance by contacting Scottish Music Information Centre www.smic.org.uk.

Charles-Edouard Platel wrote a piece of music called "Sawlogy" Or the "languor of saws". This work obtained the 2nd price of the MUSICA NOVA competition, Prague 2007. Charles-Edoardo states that "The musical saw or blade noise, lends itself particularly to evoke the melancholy moose a desolate soul, or a state of sublime meditation. Instead, saws work suggests optimism rather invigorating workshop. The play 'the languor of the saws' evokes an unexpected visit to a chorus of saws musical saws in a quartet of gears". The 8 minute piece can be heard at http://charles.platel.pagesperso-orange.fr/music/sawlogy/index.htm .

Scott Munson - an American composer wrote "The Undeterred” (2007) for the unusual combination of piano, voice and musical saw, premiered at Carnegie recital hall and was later repeated at New York’s Lincoln Center Library for the Performing Arts.

F L Duncan Wedd in 2008 composed "Shaken with the wind"

Barry Booth  in 2009 composed "Reminiscences of Wales". This piece was originally written as a feature for solo musical saw played by Richard Watson and the BBC Concert Orchestra. It was first performed in a St. David's Day broadcast of 'Friday Night is Music Night' on BBC Radio 2. In this version I have given the solo part to an alto flute but it would equally suit several other instruments.

Simone Spagnolo  has written a 'Concerto for Musical Saw, String Orchestra and Pandemonium of Saws'. He is still negotiating for a performance with a string orchestras anyone interested should contact him through his web site. Simone is also responsible for writing a  substantial academic essay titled 'Musical Saw: Mechanics and Notation'.

Benjamin Till  in 2010 wrote a section for musical saw in the BBC commissioned work for Yorkshire Day. Benjamin's "Symphony for Yorkshire" is created to reflect the different parts of the UK's biggest county; the industrial landscapes of South Yorkshire, the moorlands of West Yorkshire and the seaside and fishing traditions of Humberside and North Yorkshire. I was the musical saw soloist for the symphony which was first performed on the 1st August 2010.

Charles Hindmarsh  - in 2011 wrote  "March of the Sawyers", based on  a brass band style of march to promote a book for the children's author Alan Snow.

Scott Munson -  "Another Earth" (2011) a composition, with musical saw for American science fantasy drama film.