https://mathics.github.io/ is open source partial clone. Frankly with out a source of income it wouldn't be what it is today.
Sympy or Sage are much better examples of open source computer algebra systems, but they lack the pattern-matching weirdly-lispy language design of Mathematica (the Wolfram language, which while certainly weird, is very powerful).
Not sure what else is different, besides using Julia as the glue language, rather than Python/Cython.