High systolic blood pressure (SBP) causes cardiovascular disease (CVD) and is associated with mortality from other causes, but conventional multivariably-adjusted results may be confounded. Here we used a son’s SBP (>1 million Swedish men) as an instrumental variable for parental SBP and examined associations with parents’ cause-specific mortality, avoiding reverse causation. The hazard ratio for CVD mortality per SD (10.80 mmHg) of SBP was 1.49 (95% CI: 1.43, 1.56); SBP was positively associated with coronary heart disease and stroke. SBP was also associated positively with all-cause, diabetes and kidney cancer mortality, and negatively with external causes. Negative associations with respiratory-related mortality were probably confounded by smoking. Hazard ratios for other causes were imprecise or null. Diastolic blood pressure gave similar results to SBP. CVD hazard ratios were intermediate between those from conventional multivariable studies and Mendelian randomization and stronger than those from clinical trials, approximately consistent with an effect of exposure duration on effect sizes. Plots of parental mortality against offspring SBP were approximately linear, supporting calls for lower SBP targets. Results suggest that conventional multivariable analyses of mortality and SBP are not substantially confounded by reverse causation and confirm positive effects of SBP on all-cause, CVD and diabetes mortality.