Frenulum (Penis string as you mentioned) gets cut and bleed when penis front skin is very tight and not sliding back easily in sexual act.
sometimes bleed happens, if its pulled back excessively resulting in frenulum tear.
Next Steps
You report for sexologist examination to examine the tightness of foreskin and status of frenulum. After examination, if required small surgical procedure like Circumcision/ Frenulectomy will be suggested.
Health Tips
Meanwhile use of Lubic or KY Jelly during sex play may prevent such occurence.