sed -E -e "s/$(aspell list <file | sort -u | paste -s -d'|' |
sed -e 's/^/\\b(/; s/$/)\\b/' )//g" \
file > newfile
This uses command substitution $(...) to insert the output of aspell list <$file into a sed search and replace operation.
aspell's output is also unique sorted and paste is used to join each line with |. Finally it is piped through sed to makeadd \b word-boundary anchors as well as open and close parentheses. All of which constructs a valid extended regular expression like \b(word1|word2|word3|...)\b to use as the search regexp in the sed search and replace command.
You can test itthe result of the entire command with, e.g., diff -u file newfile
AFAIK, aspell doesn't have an auto-correct mode. This is probably a Good Thing.