SegWit does not remove signature data from transactions. SegWit creates a bigger block, and in the bigger block all transactions contain signatures. Transactions without signatures continue to be invalid and signatures continue to be committed in blocks.

SegWit allows partial validators who do not check signature validity to do so without downloading the signatures themselves. This does not make invalid transactions valid. It does not make invalid blocks valid. It does not make invalid signatures valid. It does not make transactions without signatures valid. It does not remove signatures from blocks, as all block content continues to be committed in the block header. SegWit simply lets you verify non-witness transaction data without downloading (then discarding) the witnesses, which solves the problem of light clients having to download things they don’t care about.