I am not really sure you would want to do such a thing. Anyway, you could use Replace(). ie:

DECLARE @t VARCHAR(MAX)
    = '"emailTexts": [
  {
    "id": 1,
    "body": "Dear Sir\r\n Greetings!\r\n ThankYou",
  }';

SELECT REPLACE(@t, '\r\n', '');

Or (to deal with all occurrences of \r \n \t):

SELECT REPLACE(REPLACE(REPLACE(@t, '\r', ''),'\n',''),'\t','');

PS: If you would do this on large data then consider creating a CLR function instead.