I am wondering if the Samaritans observe the Sabbatical year differently than most the "Masoretic" Jews. If so, how?
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I realise that this won't fully answer your question, but until somebody with experience of Samaritans weighs in, I can tell you that both Jews and Samaritans determine the agricultural year from the seventh month and not the first. This means that, unlike various other festivals, Jews and Samaritans "celebrate" the Shemittah year at the same time, and celebrated the Yovel year at the same time too (when this was something that Jews actually celebrated). Unfortunately, I don't have anything to add about the means by which they do this, though it wouldn't be hard to figure out some differences. Many of the laws that pertain to the rabbinic observance of these festivals are marked deviations from the literal interpretation of scripture. They can be found for the most part in Tractate Shevi'it of the Mishna, and range from the rabbinic (interpretation of and) ban against eating that which grows naturally from the ground (ספיח) to Hillel the Elder's prozbul.
The very little that I am able to share about Samaritan practices during this time, I learnt from the following:
On p.74, he produces Samaritan texts from the 16th and 18th centuries to testify to their using the seventh month, like Jews do, instead of the first.