"Is there a regex function that can extract matched strings and delete them after?"
Not really.
You could do something like this with regexprep and dynamic expressions to store the matched data in a workspace variable, but this will be slow, complex, and rather fragile.
One simple and efficient workaround would be to use both the match and split outputs: this example matches and removes the digits, leaving only the alphabetic characters:
>> S = 'abcd1234efghi6789jklm';
>> [X,Y] = regexp(S,'\d+','match','split');
>> Z = [Y{:}] % the new string with substrings removed
Z =
abcdefghijklm
>> X{:} % the matched substrings
ans =
1234
ans =
6789
