"In 2016, the authorities started saying things in meetings like, 'We will kill people we catch stealing'," the report cited the witness as saying.
Others killed without a trial were accused of stealing bananas, sugar cane or a motorcycle.
According to the report, based on 119 interviews with family members, witnesses, officials and others, at least 11 men were killed for using illegal nets while fishing on Lake Kivu in Rubavu.
FAMILIES SILENCED BY FEAR
HRW also documented the case of two men who were killed by civilians after being encouraged to do so by local authorities.
Family members were left terrified and warned to keep silent.
One widow, taken to the body of her husband after he was in the forest, said: "The soldiers told us not to be sad and not to cry. They said if we dared to cry, we would risk being shot."
Another witness to the killings told HRW: "We have no right to free expression. If we talk about this, we will end up in prison or disappear."
Rwanda has been held up as an African success story for advances in its economy, infrastructure and security since the 1994 genocide in which some 800,000 people, mostly Tutsis, were killed.
But alarm has risen in recent years over a crackdown on freedoms and opposition groups.
A report by Amnesty International last week warned that two decades of repression had created a "climate of fear" ahead of next month's presidential election.