How to select and insert into new table without duplicate value?

You're doing a cross join on inequality which will generate an huge amount of (duplicate) rows.
Instead you should do a LEFT JOIN on equality and filter out the null rows.

I'd rewrite it to:

INSERT INTO table2 
  (`student_id`, `studentname`, `Regno`, `class`, `date`, `session`
   , `status`, `teacher_id`) 
SELECT t1.* FROM table1 t1
LEFT JOIN table2 t2 ON (t1.student_id = t2.student_id)
WHERE t1.`date` BETWEEN '2011-01-01' AND '2011-05-19' 
AND t1.`class` = 'AAA'
AND t2.student_id IS NULL 

Here student_id is the primary key for both t1 and t2. If the PK is (student_id + teacher_id) then the query becomes:

INSERT INTO table2 
  (`student_id`, `studentname`, `Regno`, `class`, `date`, `session`
   , `status`, `teacher_id`) 
SELECT t1.* FROM table1 t1
LEFT JOIN table2 t2 ON (t1.student_id = t2.student_id 
                        AND t1.teacher_id = t2.teacher_id)
WHERE t1.`date` BETWEEN '2011-01-01' AND '2011-05-19' 
AND t1.`class` = 'AAA'
AND t2.student_id IS NULL  /*<<-- this stays the same provided student_id is  
                             <<-- defined as `NOT NULL` */

Here's how it works.
First we select all rows where (t1.student_id = t2.student_id); this lines up all matching rows in t1 and t2.
Because it's a left join, rows that are in t1 but NOT in t2 will have null values in the t2 columns.
By only allowing rows where t2.student_id IS NULL we only select rows from t1 that have no matching row in t2.