Can you join the military with a bicuspid valve replacement?

Valve surgery. To my knowledge, any type of cardiac surgery generally precludes service in the military. You should contact a recruiting office for a specific answer.
Unlikely. I'm not in the military and I don't know their rules, but I would be surprised if they allowed it.

Related Questions

Is bicuspid aortiic valve replacement similar to mitral?

No. Two different valves with different shapes and function. The aortic valve should have three leaflets or cusps but some people are born with only two and hence have a bicuspid aortic valve. They are predisposed to aortic stenosis and aortic regurgitation. They also have a higher incidence of aortic coarctation.
Valve replacement. The surgery replaces the valve with either a mechanical or animal tissue valve. This is done on a heart lung machine. The valve takes the place of the damaged valve and the patient lives their life with a new disease 'artificial valve' with its own set of problems. The obstruction or valve leak of the diseased valve is corrected by the artificial valve. Sometimes blood thinners are needed.

Is bicuspid aortiic valve replacement like mitral valve replacement?

NO. Aortic valve replacement in a patient with a bicuspid aortic valve may require repair of an ascending aortic aneurysm if present. Although valves are sewn in place the same, the location is totally different with particular anatomic differences. The mitral closes in systole and the aortic valve in diastole. For the mitral need to actually open the heart. For the aortic its done thru the aorta.