I am going to Hong Kong and wanted to travel to Shenzhen for a day trip.

No, you cannot do that. However, you can apply for a 5 days Shenzhen visa on arrival at designated border crossings. My suggestion is to think about taking a direct morning ferry provided by CKS from Hong Kong to Shekou port in Shenzhen because it is a comfortable way of travel and also the waiting times at Shekou visa office are shorter than those at overland border crossings. You should just be aware of the Shekou visa office opening times: 9:00 - 13:00 & 14:30 - 16:30.

After your stay & exploration in Shenzhen, you can return to Hong Kong taking any mean of transportation (high speed train included) and by taking any border crossing.