Such hard evidence as there is points to the Saperias having come from the Gubernias of Suwalki & Lomza (a Gubernia being an administrative division of the Russian Empire). Fair records exist from this area, which are reasonably available thanks to the efforts of the Church of the Latter Day Saints; furthermore many of these records have been indexed by Jewish Records Indexing - Poland and The Litvak SIG. A search of these records shows many instances of the surnames Sapir, Sapira, Sapiro and Szapira. Here is an example of a signature from a marriage certificate:
The surname in question is apparently Sapir; it seems that the "ia" at the end of the Sapir in the document may be due to the grammatical usage and not intrinsic to the name -- endings vary in Polish and, unlike in English, proper nouns also get modified. The record was sent to me by Neil Mayle, and contains further images of Polish records. Given that the records were written predominately in Russian, and that the Russian and Polish alphabets contain more than the 26 letters of English (Russian has 33 and Polish 32 letters), it seems highly likely that Saperia is a variant form of Sapir, with the spelling change to accommodate an accented vowel sound. Study the Polish alphabet and Russian alphabet and come to your own opinion.
Since it may well have been that the first Saperias were unable to write English, the likelihood of a phonetic spelling is increased. If you view carefully the UK naturalization papers for Nathan & Harris Saperia in 1986, both signed the Oath of Allegiance (2nd page) with a mark (X) rather than their name. Further, Harris has his surname spelt Saperie on the birth records of his second and fourth children and Sapiere on the record of his third.
In the Russian Pale of Settlement, Jews were required to take surnames at various times in different countries, having previously been known as by given name and father's given name. Czar Alexander I unsuccessfully mandated that Jews adopt surnames in 1804. However, it was not until 1836 that all Russian Jews had surnames. By 1844, they were compelled to enter their names in a public register. Surnames were chosen according to various schemes: profession, town of birth, physical appearance or purely ornamental. It is generally accepted that those with Spira or Shapiro type names originated from Speyer in Germany, which welcomed Jews in the 11th century at the behest of Rudiger, Bishop of Speyer. As an example, source documents from this period make reference to Reb Kalonymos ben Reb Yosef haKatan miShpeira (mi - from; Shpiera - Speyer). As outlined in the history section, it is possible our ancestors moved from Germany to Poland and Lithuania in the 16th century and would still have carried the tag 'from Speyer' in their name (names being largely of the form A, son of B, from C). Alternatively, Saperia may have been an ornamental name derived from the Hebrew word for sapphire. Letters received from Mr S. Szapira and Mr M. Freedman argue for Speyer and sapphire respectively.
Whilst our surname is not common, is has a curious persistence amongst those who emigrated to Leeds from the Suwalki area. This strongly suggests that the various Saperia family trees are linked and that those who emigrated were following in the footsteps of their relatives, though we have not been able to establish this from records.
Aswell as sharing a surname, the Saperias evidently favoured a limited selection of given names. Amongst the girls, Rachel, Fannie and Ann(ie) were exceedingly popular, whilst Louis, Harris and Nathan recur as choices for boys. A word of caution: there was a brief fashion for 'Simon' in the 1890's, which faded rapidly as all the unfortunate babies died in their first year!