Javascript does not support possessive quantifier like \w{2,}+ but apart from that your pattern will not give you the desired results after replacing.
Note that the space ( ) does not have to be between parenthesis to make it a group, you have to escape the dot \. to match it literally and {1,} can be written as +
What you might do is repeat matching 2 or more word characters followed by a dot and 1+ spaces OR match 1 or more times a non word character except for a whitespace char.
In the replacement use an empty string.
(?:\w{2,}\.[^\S\n]+)+|[^\w\s]+
See a regex 101 demo.
const regex = /(?:\w{2,}\.[^\S\n]+)+|[^\w\s]+/g;
const s = `DR. Tida.
prof. Sina.
DR. prof. Tida.`;
console.log(s.replace(regex, ""));
Although this part \w{2,}\. can obviously match more than just titles.
You can also list using an alternation what you want to remove to make it more specific:
(?:\b(?:DR|prof)\.[^\S\n]+)+|[^\w\s]+
See another regex101 demo
{2,}+supposed to mean?