It depends what you mean.

> I need to modify a picture with pink color.

or more naturally,

> I need to modify a picture with pink.

> I need to modify a picture with the color pink.

This sentence could be interpreted as saying you need to modify a picture by adding the color pink, either to change an existing color to pink or to mix it with pink (e.g. a black-and-white version of the Komen Foundation logo). It could also be interpreted as saying you need to modify in some unspecified way a picture which already contains the color pink (e.g. a picture of a carnation).

>I need to modify a picture using pink color.

i.e. 

>I need to modify a picture using pink.

>I need to modify a picture using the color pink.

This sentence explicitly says you will apply the color pink to the picture, but I don't think sounds as natural as using "with."

The last example,

>I need to modify a picture by pink color.

is not typically used in English.