You can send SWIFT transfers from a Chinese bank account but will need to provide documentation to the Waihuiguanliju (Foreign Exchange Management Bureau) about where it came from, eg. employment contract, etc. You can do this at any bank branch in my experience, though they have a shared SWIFT code. I've done it with a Zhaoshang Yinhang a few times before. If you have lost your documentation then you can get a company to send you the money via the same method, eg. for providing nebulous online services. This requires an invoice issued from a foreign company. Leave your name off the invoice. Once that documentation is present, the bureau should approve the transfer to a company-title account overseas.
A second option is opening a Chinese bank account overseas (eg. ICBC) and then transferring from China to that account. This is probably a pain in the ass practically speaking though as last time I checked international transfers are not possible to do on Chinese internet banking and this method first necessitates leaving the country and probably returning.
Another option as mentioned is using Yinglian (China UnionPay) cards outside of the country, though then you are facing daily withdrawl limits and will need to waste a lot of time at the ATM.
You can also try Bitcoin as Xiefei suggested, though this exposes you to a lot of volatility if you buy and hold plus is technically challenging and can be risky if you don't know what you are doing. If you go this route, I would recommend executing in smaller amounts over a period, rather than all at once to limit your market exposure.
Finally you can convert to USD or EUR cash. Large amounts of high denomination notes actually don't take up that much physical space. There are people in town who can facilitate this. They used to hang around outside of the Bank of China on Beijing Lu, there are undoubtedly more people also. However, you are going to be crossing borders with more money than you are supposed to, which creates risks.
Outside of the above, these days you can exchange CNY cash in many places for foreign cash, eg. most of Southeast Asia, any major tourist city in the world.
Overall, the 'try to only accrue as much RMB as you actually need' strategy seems a time-honored one.
As it seems the original poster has the problem of 100s of 1000s of USD worth of RMB (house sale?) then if all the income is reported to the US and is no problem, your easiest method is SWIFT. If it's not all reported, and you don't want to report it, then I would heartily recommend leaving your money in Chinese banks internationally. With the amount of money you have but don't want to report in the US, you probably don't want to use SWIFT since that's heavily monitored by the US and its allies - every transaction on SWIFT since "at least 2001" is stored by them. Transferring between Chinese banks is less visible, so that's one strategy. However, Chinese banks in the US are obliged to comply with US domestic law. Chinese banks internationally care less about US demands. I would recommend opening an account with a Chinese bank in a tertiary jurisdiction and transferring the money there in portions as needed, which allows you to convert it to a major international or the tertiary jurisdiction's local currency as well as leaving it in RMB. The US will have a harder time seeing the money, and you can pull it out via debit or even credit card. To truly repatriate the money you may need either a few trips with cash and/or buying bulk gold for resale, or a shell company, which is getting in to truly painful territory. Hong Kong is good for companies in a pinch (2-3 hours should be adequate) though for any protection whatsoever you will need someone else to act as the director and your name off the company documentation. Long term - if you expect to generate more offshore revenue that you don't want to report - your best solution may be to change citizenship.