But the warranty not start from the date they deliver? As what the seller told me

Depends on seller. They could take the money from you as deposit for the said items that you pre-booked and only issue an official receipt when you finally ready to accept deliveries. It's basically a trust issue rather than anything.
I dont think it is necessary to get the warranty card chopped anymore. Most if not all would just require the warranty card (Im guessing to avoid parallel import for some brands) and an official receipt (some shops) from the shop that you made purchase.

Recently bought 2 Khind stand fan from Lazada Senheng and both have problem fitting the grills, probably due to shipping issue. I only brought along the warranty card and they kindly replaced the grill when I pay them a visit.