SELECT @id:=@id+1 AS id,
       `brand`,
       `group` 
FROM
(SELECT
  `id`, 
  `brand`,
   SUBSTRING_INDEX(SUBSTRING_INDEX(`group`, ',', n.digit+1), ',', -1) AS `group`
FROM
  Table1
  INNER JOIN
  (SELECT 0 AS digit 
   UNION ALL SELECT 1 
   UNION ALL SELECT 2 
   UNION ALL SELECT 3  
   UNION ALL SELECT 4 
   UNION ALL SELECT 5 
   UNION ALL SELECT 6) n
  ON LENGTH(REPLACE(`group`, ',' , '')) <= LENGTH(`group`)-n.digit
  Order by ID,`group`) AS T,(SELECT @id:=0) AS R;

输出

id  brand   group
1   adidas      1
2   adidas      2
3   puma        1
4   asianone    1
5   asianone    2
6   asianone    3

演示
http://sqlfiddle.com/#!9月29日C2月31日
有关解释，请转到此链接并查看我的答案
mysql：将列数据转换为行

请使用php explode（）函数。它可以将字符串拆分为数组。
语法：“explode（separator，string，limit）；”

select
   brandstable.id,
   brandstable.brand,
   SUBSTRING_INDEX(SUBSTRING_INDEX( brandstable.`groupname`, ',', numbers.n), ',', -1) `groupname`
from
  (select 1 n union all
   select 2 union all select 3 union all
   select 4 union all select 5) numbers INNER JOIN brandstable
  on CHAR_LENGTH(brandstable.groupname)
     -CHAR_LENGTH(REPLACE(brandstable.groupname, ',', ''))>=numbers.n-1
order by
  id, n

replace your tablename with brandstable.