I have yet to find any description of the repertory of the spitzharfe, or any mention of it in the title or instructions of any notated music. However we might assume that it was used for the same repertory as the davidsharfe or keyboard instruments at that time.
The sound of the spitzharfe is very jangly and distinctive - Adlungs in 1758 used the spitzharfe as a reference to describe the sound of the spinet- or lute-stop on a harpsichord, which plucks close to the end of the string.
It is hard to pinpoint the disappearance of spitzharfen from the musical scene, mostly because we have so little evidence from when it was in common use. Two early 19th century texts say that the spitzharfe is almost obsolete. The Beitrüge zur Geschichte Deutschen Alterthums in 1837 says that the instrument is extinct, but that there is a possibility of finding it still out in the villages.
The Museum of the University of St Andrews instrument has a fragment of notation as part of its decoration:
Simon Chadwick, St Andrews, Scotland.