Do you have to clip off dead parts of a branch?

[PepperZ]

http://imgur.com/a/L7mWJ
 
It's a bit out of focus, but you can see the tips of both plants are kind of dark brown and might be dead. I don't know if I'm supposed to cut them clean off or leave them? These are overwinters ftr.
 
I haven't bothered because I didn't want to shock them more after the initial cutback and the end of summer and they have done seemingly fine(have grown overall and plenty of foliage from other parts of the plant).
 
Basically, just for future reference, is there something I'm supposed to do when I see the tips of where I cut them turn dark brown? The rest of the branch won't die off will it(I imagine no given how long ago it got cut). 
 
Will it just form side shoots or something in the summer?

 

[floricole]

You should cut the dead wood, this prevents mushrooms, diseases and insects from settling. The ideal which is not always possible is to cut just at the top of a bud that is oriented towards the outside of the plant

 

[solid7]

You could clip it, or just let it be.  Either way, same result...

 

[PepperZ]

You should cut the dead wood, this prevents mushrooms, diseases and insects from settling. The ideal which is not always possible is to cut just at the top of a bud that is oriented towards the outside of the plant

What do you mean at the top of a bud? @@; got an graphic? 
 
Do you know why some tips end up dying like that in the first place?
 
Thanks.

 

[Powelly]

just cut the brown off

 

[floricole]

What do you mean at the top of a bud? @@; got an graphic? 
 
Do you know why some tips end up dying like that in the first place?
 
Thanks.

 
If you cut like "a" there is no bud that will appear on the rest of the stem, so no sap call and it will dry

 

[The_NorthEast_ChileMan]

just cut the brown off

 
^^^Persactly!^^^
 

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[floricole]

Why do half good when you can do it right

 

[PepperZ]

 
If you cut like "a" there is no bud that will appear on the rest of the stem, so no sap call and it will dry

That is a great graphic and probably accounts for why the tips dried out. Why is D wrong btw? I get that the difference is the direction of the cut but what is undesirable about that? Thanks a ton btw.

 

[floricole]

That is a great graphic and probably accounts for why the tips dried out. Why is D wrong btw? I get that the difference is the direction of the cut but what is undesirable about that? Thanks a ton btw.

 
Simply to prevent water from flowing at the base of the bud.