I think you might be disappointed using a jeweler's saw for block work. a coping saw with fine blades might take the work. maybe I don't understand the size blocks you are cutting, but jeweler's saw blades are not going to follow a long deep cut perpendicular and the harder you saw, the more the blade heats and distorts.
a jeweler's saw is made for fine cutting and getting into places another saw might not reach.
a razor saw for straight cuts. teeth range from about 40 to 52 per inch. block work might respond well to a Japanese style pull saw.
https://en.wikipedia.org/wiki/Piercing_saw
https://en.wikipedia.org/wiki/Coping_saw
https://en.wikipedia.org/wiki/Japanese_saw