The man had been in Stravanan Off Sales in Stravanan Road, Castlemilk, with two friends at around 8.40pm on Monday, June 23 - and he was attacked as he left the premises.
Police say he was initially approached by a man who, for no apparent reason, pushed him to the ground.
Another man appeared and stabbed him a number of times. Both suspects then ran off.
A few local people went to the aid of the victim before an ambulance arrived.
He was taken to the Victoria Infirmary suffering from injuries to his head, abdomen and leg.
He remains in hospital where his condition is described as serious but stable.
The first suspect his described as white, in his late teens to early 20s and he was wearing a long sleeved black top and cargo style trousers.
The second suspect was in his 40s, bald and he has a stout build. He was wearing a black t-shirt and black knee length shorts.
Detective Constable Lyndsay Connor, of Cathcart Police Office, is appealing for witnesses.
She said: "At this time, we are trying to establish a motive for what would appear to be an unprovoked attack. The victim's friends were not assaulted and no attempt was made to rob the victim.
"Although a few people went to his aid, they did not witness the assault and I am appealing to anyone who was in the area of Stravanan Road around 8.40pm on Monday evening and saw the attack to come forward. I would also ask anyone who recognises the description of the suspects to get in touch."
Anyone with information is asked to telephone the CID at Cathcart on the non emergency telephone number 101.
Alternatively telephone Crimestoppers on 0800 555 111 where anonymity can be maintained.