Probably only by a private boat charter.
And to do that LEGALLY, one would have to go through customs and immigration on Anguilla and since the ferries shut down I do not believe Anguilla would take someone from SXM since Anguilla closed their borders March 20 as stated in the article.
This in ONLY good if one is already on Anguilla.
"
US citizens who have been in Anguilla since the closure of the borders on March 20 are being given an opportunity to leave the island."