Q:

Is it allowed to destroy political billboards?

I see that political posters in Germany during election get destroyed all the time. For example, NPD posters are always teard down or on a ground. Merkel's picture is often with beard and mustache. People write something or tear down AFD posters. Etc
So, is this accepted political fight? Am I allowed to destroy political posters? If not, what is the punishment?

A:

No, you are not allowed to destroy or deface other peaple's property (§ 303 StGB) 

the attempt to do the same is also punishable 

To whom it belongs to is irrelevant. 

The Freedom of expression is restricted by Artical 5 (2):

the provisions of general laws

of which § 303 StGB is only one of

in the right to personal honour

as well as § 185-188 Criminal Code (StGB) - Insult and Defamation 

So insulting someone because you disagree with their viewpoint also exceeds the Freedom of expression. 

Section 303 - Criminal damage 
(1) Whosoever unlawfully damages or destroys an object belonging to another shall be liable to imprisonment not exceeding two years or a fine.
(2) Whosoever unlawfully alters the appearance of an object belonging to another substantially and permanently shall incur the same penalty.
(3) The attempt shall be punishable

Article 5 [Freedom of expression, arts and sciences]
(1) Every person shall have the right freely to express and disseminate his opinions in speech, writing and pictures and to inform himself without hindrance from generally accessible sources. Freedom of the press and freedom of reporting by means of broadcasts and films shall be guaranteed. There shall be no censorship.
(2) These rights shall find their limits in the provisions of general laws, in provisions for the protection of young persons and in the right to personal honour.
(3) Arts and sciences, research and teaching shall be free. The freedom of teaching shall not release any person from allegiance to the constitution.

Section 185
  Insult
An insult shall be punished with imprisonment not exceeding one year or a fine and, if the insult is committed by means of an assault, with imprisonment not exceeding two years or a fine.
Section 186
  Defamation
Whosoever asserts or disseminates a fact related to another person which may defame him or negatively affect public opinion about him, shall, unless this fact can be proven to be true, be liable to imprisonment not exceeding one year or a fine and, if the offence was committed publicly or through the dissemination of written materials (section 11(3)), to imprisonment not exceeding two years or a fine.
Section 187
  Intentional defamation 
Whosoever intentionally and knowingly asserts or disseminates an untrue fact related to another person, which may defame him or negatively affect public opinion about him or endanger his creditworthiness shall be liable to imprisonment not exceeding two years or a fine, and, if the act was committed publicly, in a meeting or through dissemination of written materials (section 11(3)) to imprisonment not exceeding five years or a fine.
Section 188
  Defamation of persons in the political arena
(1) If an offence of defamation (section 186) is committed publicly, in a meeting or through dissemination of written materials (section 11(3)) against a person involved in the popular political life based on the position of that person in public life, and if the offence may make his public activities substantially more difficult the penalty shall be imprisonment from three months to five years.
(2) An intentional defamation (section 187) under the same conditions shall entail imprisonment from six months to five years.

Sources:

§ 185-188 Criminal Code (StGB) - Insult and Defamation
§ 303 Criminal Code (StGB) - Criminal damage 
Article 5 - Basic Law for the Federal Republic of Germany 

