Argthtjtr

I have recently joined a game and there were several instances where the dungeon master just shot down any idea that didn't fit her plot.

We were supposed to have this encounter in this forest with a bear and the druid cast animal friendship, but the game master just ruled that since we were in the bear's territory it was going to keep attacking us. But she ruled that Animal Handling was enough to distract the beast so that we could escape.

In another case we were suppose to find a doll for a girl and we found it with severe damage. I thought of casting mending, but she told me no, saying that the damage was too high. However, she allowed our local healer to use her medicine skill since it included sewing up torn parts.

There were other cases like this, and it is starting to get on my nerves as I play as a spellcaster. In most of the cases, she gives a rather reasonable excuse, like in the mending case the damage being too high, and in the animal friendship case the bear is not going to stop attacking something in its territory even if it believes they don't pose a threat.

The fact that she shoots down the ideas of me and the local druid is not the problem. Rather, my problem is whenever someone tries to accomplish what me and the druid tried to do via a skill check, she allows it to happen.

The setting is that we are a group of adventurers in a village that is mostly cut off from the world, solving problems for the village by doing quests posted at the local branch of the adventurers' guild.

How can I reason with my game master so that she allows me to be something more than a combatant with a fancy hat? I have not talked with my game master yet. I am not sure how to approach her about this issue without sounding accusative and angry.

There's no solution apart from talking to your DM.

Your DM apparently likes to solve things in a more mundane way and if this was accorded between the DM and the players it would be no problem at all. However, you said there are 2 spellcasters in your group and their magical solutions have been shot down with no apparent reason. You could argue that the spells were made exactly for that, solving problems quickly, usually a limited number of times per day (don't try saying "the rules" allow you, often pisses the DM and the DM is "the rules").

Ask why the DM didn't let both of you solve the problems with your spells that were proper for these situations and try to convince the DM that solving problems with spells is exactly what a spellcaster is made for. Nothing will be solved without you talking to your DM.

That can be rough. As folks have said, the GM can like the mundane but letting in spellcaster without telling them ahead of time there may be limitations in place can be frustrating. By allowing these characters in, the GM has decided, however tacitly, magic users in the world exist and perhaps abound. You sound poised, reasonable and well meaning in your above post, having thought out how your approach could be perceived by said GM. As others have said, a direct approach, 1 on 1 or with the druid, if they feel the same, can be the way to go if you feel the GM is approachable. If the druid is with you and you have a more open forum, this can strengthen your point of view, but if you feel like this could be viewed negatively, maybe each of your voicing your concerns at a different time might be less harsh. As folks have said, the GM may never know there's a perceived issue if it isn't known. In that vein, maybe you can rummage about a bit:

Try asking how the GM views magic in the grander scheme of the game. Magic can be the ultimate plot device, so how does you GM see it affecting the world and what its role is, from mundane things, to grander designs. Ask them about specific instances. Is this cloistered town you're in unaware of magic? That's something you, as PCs, should be aware of so you can temper how you approach the plot. Finger wiggling among superstitious folks could bring about sticky situations. This could allow you to gain her perspective on your role as a magic user without being perceived as accusatory and give everyone a better idea of how the world works with magic in it.