Do I need a visa if I intend to leave Guangzhou airport to Hong Kong by train?

Mark, what is your route? If you fly from another country to Guangzhou and then take the conventional train to Hong Kong, you can make use of the 144h visa-free transit in Guangzhou.

My route is Italy - Guangzhou - Taipei. I, most probably, won't take flight Guangzhou - Taipei, and plan to visit Hong Kong from Guangzhou instead.

I don't need visa to HK but need visa to China. I'm not really keen to stay in China, just take a train to HK.

Doesn't transit visa require me to stay in transit zone at the airport?

If you will be coming back to Guangzhou to take the flight to Taipei then pretty much the only way you can do it is by taking the Guangzhou-Kowloon Direct Train (the conventional train) to Hong Kong, and fly from HKG to CAN. Without a visa you won't be able to take the high-speed rail to HK and you can't get to Guangzhou from HK by anything other than air.

If you won't be going to Taipei, then one-way travel from Guangzhou to HK is fine on the conventional train.

If you don't have a visa then you would need your confirmed train ticket to Hong Kong in your hand when you check-in for your flight to Guangzhou.