A Norfolk and Suffolk Foundation Trust report says the number of SIs rose from 161 in 2012-2013 to 228 in 2014-2015.
The report says a significant number of these serious incidents involved unexpected deaths.
The trust said staff felt free to report any possible problems.
SIs can include a wide range of incidents and are reported to help health trusts learn lessons and prevent future incidents.
The report highlighted five deaths within Wellbeing Services, which provides support for people with mental health problems such as depression, between December 2014 and March 2015 and these were being reviewed by the trust.
Michael Scott, the chief executive of the trust, told the BBC: "The board looks closely at all the data, and we look at national benchmarks. We remain a high reporter of incidents, but the majority are 'low harm' incidents.
"Staff do speak up and record incidents when things go wrong."
A spokesman for the Campaign to Save Mental Health Services in Norfolk and Suffolk said: "Some of this rise may be due to changes in reporting, but an increase of more than 40% in only two years is deeply worrying."
A mental health trust has seen a 41% rise in the number of serious incidents (SIs) - which can include unexpected deaths, injuries or security issues - over three years, new figures show.