Which airlines with routes connecting Vietnam and China have free cancellations and can be booked online?

Since you’re not using an agency, you’ll need a credit card with a big enough limit. In order to get the confirmation in order, they will need to get the charge approved and posted to your account. When you cancel, you’ll get a credit from them. Time it so that the debit and credit fall within the same billing cycle to avoid having to make a payment or accrue interest. Cancel well in advance of the flight, don’t check in, and use the same website you used to book the ticket.

Booking with a Chinese carrier can be expensive. You’re getting the money back (probably), but there will be a sizable charge (could easily be several thousand RMB) posted to your card. You may also incur foreign transaction or currency conversion fees from your card provider, quite possibly both coming and going, and these will not be refunded.

Air China will let you cancel full fare economy class tickets for free, as long as you don’t wait until the last minute to do it. I put together a sample ticket on their site from Ho Chi Minh to Guangzhou, leaving May 7 and returning May 8. Full fare economy price: ~8500CNY (~1400USD). To see the details of their cancellation policy, you have to actually select an itinerary through the booking interface, because the refund policies vary by ticket type.

1.3 Rebooking Fee (per change): free to change/rebook. Passengers will also need to pay the difference in fare (if any). For tickets booked on Air China official website, rebooking can be done through the official website or 95583. For tickets booked through other channels like Taobao flagship store, rebooking can be done through 95583 only. [95583 is a special service number you can call only via a Chinese mobile carrier.]

1.6 Refund fees (children’s ticket are subject to the same standard that apply to adult tickets): Free to refund. For refunds of partially used tickets, the refund amount will be calculated after deducting the fare and taxes corresponding to the flight segment(s) used.

The official Air China refund policy states (emphasis added):

10.3 Voluntary Refunds
10.3.1 If you are entitled to a refund of your Ticket for reasons other than those set out in 10.2, the amount of the refund shall be:
10.3.1.1 if no portion of the Ticket has been used, an amount equal to the fare paid, less any reasonable service charges or cancellation fees;
10.3.1.2 if a portion of the Ticket has been used, the refund will be an amount equal to the difference between the fare paid and the applicable fare for travel between the points for which the Ticket has been used, less any reasonable service charges or cancellation fees.
10.5 Right to Refuse Refund
10.5.1 We may refuse a refund where application is made after the expiry of the validity of the Ticket.
10.5.2 We may refuse a refund on a Ticket which has been presented to us, or to Government officials, as evidence of intention to depart from a country, unless you establish to our satisfaction that you have permission to remain in the country or that you will depart from that country by another carrier or another means of transport.

That last bit is most likely intended for trying to cancel the return trip after arriving in China, but could technically be employed in your case.

The Air China website is actually quite good as Chinese e-commerce platforms go. To cancel, go to the "online check in" page, click the cancel tab, enter your information, and confirm through. If there’s some problem with the site, it shouldn’t be an issue getting English language customer support via their call centers, but you may need to make an international call as I don’t know if the Vietnam offices have English speaking reps. You can probably also cancel by logging in and viewing your details, but I can’t verify that at this time.

For a much lesser charge, ITA Matrix lists China Southern as the cheapest carrier at ~7m VND (~325 USD) (same dates and airports). Their official policy doesn’t list anything terribly specific either way about cancellations, though it does sound relatively reasonable. After actually picking out an itinerary on their site, I was able to find this (translation by Google; no link as it’s JSP generated):

Cancel
Totally unused tickets
Cancellation / Refund charges of $ 20.00 (usd).
Partially used ticket
Cancellation / Refund charges of $ 40.00 (usd).

Elong.net has a listing of the policies of the most common Chinese carriers. They’re a reputable site for English language booking of transportation within China. The copyright notice at the bottom says 2010, so I don’t know if the data is out of date. According to them, most of the carriers charge a 5% cancellation fee assuming you cancel well in advance and are flying a full class economy fare. Discounted fares have much steeper cancellation penalties. I have not vetted most of this information, but it matches my experiences with Air China and China Eastern. I also don’t cancel flights much, so take that for what it’s worth.