The region's two largest economies saw factory activity expand at a slower pace in March, suggesting that their recoveries may be losing momentum.
Hong Kong's Hang Seng index ended down 0.4% at 24,399.6, while Japan's Nikkei 225 closed 0.1% lower at 19,734.05.
The Shanghai Composite reversed earlier losses to close up 0.1% at 3,691.41.
That marks the 10th consecutive daily gain for the mainland benchmark.
Australian shares also closed higher, with the S&P/ASX 200 rising 0.2% to 5,969.08, thanks to a rally in gold mining stocks.
South Korean shares followed that trend with the Kospi index ending up 0.2% at 2,041.37 - its highest finish in six months.
China's factory activity fell to an 11-month low in March after new orders decreased, a survey indicated.
The flash HSBC/Markit Purchasing Managers' Index (PMI) fell to 49.2 in March, down from February's figure of 50.7. A figure below 50 indicates contraction in the sector.
Julian Evans-Pritchard from Capital Economics said the PMI reading was "the latest in a string of disappointing data out of China".
"Looking ahead, we expect the deceleration in growth to moderate in coming months as policymakers step up fiscal spending and carry out further cuts to the required reserve ratio and benchmark interest rates in order to prevent growth this year from slipping too far below their annual target," he said in a report.
Japan's manufacturing Purchasing Managers' Index by Markit fell to 50.4 on a seasonally-adjusted basis from February's figure of 51.6.
Asian markets experience mixed fortunes after surveys indicated weaker manufacturing growth in China and Japan.